I have 1 window and face East, but the sun is blocked most of the time by several large trees. I restained my oak a dark walnut and I LOVE it. I even put on dark counters and I'm fine.
Before:

I have a dark kitchen and live in the Pacific NW with lots of cloudy days. The key to keeping your kitchen from becoming a cave is lighting, lighting, lighting! If you have good lighting, your kitchen will be warm and rich. It sounds like you're covering the lighting issue.

If you're drawn to darker colors, like I am, then you won't regret it for a moment. I like my house to be light and bright but I love warm, rich colors. I enjoy looking at all these white kitchens and I can appreciate their beauty, but no way is it for me.

My previous kitchen faced north, and when I remodeled it I put in sort of medium light maple cabinets which I loved.

When we built our house a few years ago, we put in medium cherry cabs which have darkened some, cause that's what I'd always wanted. We have medium-light green granite, medium light beige paint, and cream colored cork flooring, as well as a cream painted island.

The kitchen faces SE, but has a 10' deep front porch which makes it somewhat dark inside, but light comes in through the triple SE facing windows over the sink in the morning at breakfast time, and we have 2 SunTunnels that provide light midday, but the room still feels dark to me in the daytime because of the cherry perimeter cabs.

I don't turn on the lights until late afternoon, because I don't need more light to see before then, unless it's overcast. Many times I've wished for my lighter maple cabinets. If I had it to do over, I'd choose lighter cabs.

Anne

I don't have very good light in my kitchen at all. I have a very small window over the sink which faces west but barely gets sun because the house next door is very close to the lot line and shadows mine. That window was that way when I took the house and I really didn't have the extra money to make it larger. It was either that or remove the other small window which faced south, and add a sliding door. I chose the door. However, even with adding the slider, it still doesn't brighten up the room substantially since the sun doesn't hit that side of the house - it hits the detached garage wall instead most of the day. I only get sun early in the morning there, and in the small window, late in the day but it's too small to make an impact.

Having said all that - I wanted dark cabinets because my home was built in 1915, and is for the most part Craftsman and has all of it's original woodwork - which had never been painted. All of it is very dark wood. I wanted to make the kitchen feel as much like the rest of the house as possible. Anything other than a dark wood seemed inauthentic to me. So, I went with Quartersawn Oak in an espresso stain (I think that's what it is, I forget already - it's been well over a year plus since it was all installed, going on 2).

I added all new overhead lighting to compensate along with undercabinet lights of course. When the overheads first came on I hated them. It felt like the sun exploded in the room lol. Now, I'm used to it and it is fine. I do wish I had not "cheaped out" in some ways on the under cabinet lights, but I had already spent something like $20K on lighting and was so angry at my electrician I just wanted to get it over already. Maybe one day I'll be able to fix what I don't like about that aspect of it - but overall, it certainly is way bright enough and I've never gotten the feeling the room is too dark.

BTW, the small window? When we began demolition we discovered it originally had been an enormous almost to the floor window that had been bricked up! And there had been another one on the same wall! These old homes when first built had big windows in them to bring in as much light as possible because electricity stunk back then :) Unfortunately, I couldn't have made it work even if I wanted to bring it back to it's original state. That, would have been one heck of an expensive window and I would have lost precious cabinet and counter space to boot.

My kitchen has only 2 windows, with another 2 nearby. It isn't a dark kitchen, but it isn't bright either. Very little direct light as we are on a narrow lot. I have walnut lower cabs, very few (2) uppers and a white pantry wall. I would not have done dark uppers in my kitchen, despite the fact that we have 28 lights in our kitchen (yes, 28). If you can do glass front uppers, no uppers, or white uppers it will make a difference. Plus lots of great lighting of course.

I'm in Upstate NY, near Lake Ontario, and we're second only to Poohpup's Pacific NW in number of cloudy days. My small galley has 2 windows, but it faces north, and we have mature trees as well. My old kitchen had cream painted cabs, pink counters and lousy lighting; I never felt I could see. My new kitchen has medium cherry cabs, slate-gray tile floor, and medium sage granite and walls. Because of the new lighting - similar to your plan- it's much brighter than the old kitchen, despite the darker color scheme. Get what you want, and light the heck out of it! Just make sure you have dimmers. All that light can be murder on a dark winter morning.

Our north facing kitchen was very dark. We enlarged two windows, took out an interior wall, and removed a roof overhang. We also added lots of recessed LED's, removed a wood ceiling (it was literally sucking the light out of the room) and designed our kitchen to have almost no upper cabs. Our countertop is light but the cabs are a medium stain. The difference is amazing. Our kitchen isn't completed yet but I often think a light has been left on in it when it's just the natural light showing. In the evenings the LEDs are perfect. We don't even have the pendants up yet. Not sure how large your kitchen is but your lighting sounds similar to ours.

Also in the Pacific Northwest and I wanted something darker than maple but not a cherry that would darken too much. Ended up with a red birch.

I did however get dark blue granite counters because the granite was just so beautiful I couldn't say no to it. I was a little worried about the color being dark. It has not been a problem.

We got several of the LED recessed lights from HD and it has made a huge difference over the single fixture in the middle. We have undercab lighting and use it more on the cabinets away from the window where it's really gloomy.

One thing I did not get was a black refrigerator. That sounded like a black hole to me. I got a stainless steel and the same with the new microwave. Will change out the d/w and stove to stainless as they wear out. Hopefully not for a while because I want to save up to get decent ones. I think the stainless steel reflects light and keeps a room looking sharp. But they do take longer to clean.

Just wanted to add a couple of points because others reminded me.

Glass cabinets will help. I have two flanking the small window. I have another one which isn't up yet due to an error during construction which will be used eventually at the breakfast area probably - but I haven't gotten around to designing that part of the kitchen yet (it's very minimal).

Also my lighting is LED. Which is why I think I was so surprised by the brightness when I first saw them. Really was different from what I was used to.

Last - I have stainless appliances which reflect light. I had black in a former home which had a kitchen that got no direct light as it was land locked in the middle of the house. Much as I liked the look for that particular kitchen I designed, it would never have worked here.

Last, my counter is a light color and the backsplash will be also once it goes in (I finally just picked it). Both of those elements help lighten up the feel of the room.

Thank you for all of your comments. I wish glass cabinets would fit in my plan but the need to hide my mess overrides the want of glass.

I'm torn between a light brown and dark brown stain color. I like the light brown but my heart goes pitty-pat over the dark brown. I'm trying to finalize my countertop choice this week so that will help solidify my decision (I think).

If your heart goes pitter patter over the dark brown cabs, then you should get the dark brown cabs! You're spending a lot of money when you remodel a kitchen. Anytime that you can makes choices the make your heart pitter patter, you should do it! Don't be scared by dark cabinets. Just really make sure you have a good lighting plan.