How you have given the containers the protection you did should work....as long as the cardboard doesn't draw a lot of snow which then melts which then turns the cardboard to mush....never mind the bulbs. As long as the containers can drain, the surface not freeze which takes temperatures down to freeze the bulbs before they develop roots, they will do fine. Bulbs by the way, once having roots can take 40 below..and that's celsius or fahrenheit. For our U.S. cousins, when Seacat quotes temperatures, they represent, when mentioning minus figures, that's minus from the freezing point....which is 32F. The true formulae is ...the C. figure X 9/5....+ 32. Since 9/5 is 1/5 away from twice the figure, we use that and subtract the fifth....or 10%. To anyone wishing to convert...its simple...take the C..celsius temperature.....double it, (X 2) subtract 10%...which is move the decimal point, and add 32º. The trick is to remember that 32 is always a plus number. So if the figure such as minus 30....becomes 60...minus 6....= 54....now subtract 32 from it....that's 32 as a plus #. So - -54 subtract 32 = 22....that's minus 22 C. Conversely, 10 C....double...= 20...minus 10%..2...= 18.. now add the 32º.....and that becomes 50 F. There are two numbers in Celsius that can be just turned around....16 C is 61 F.....and 28 C...is 82 F. Most temperatures are not exact...because in converting you end up sometimes in fractional figures. But, you're never much beyond 1 degree difference. With numbers ending in 5.,,,and 0......the end result is always true.....30 doubled...= 60...minus 10%...6..= 54...add 32....86 F. Many newer Canadians, never having to deal with fahrenheit temperatures are confused by people who still convert. But fahrenheit does give a truer, more concise view of the weather. For most of our late fall and winter and early spring, the whole country is forever in minus temperatures. This to me, weighs on the syche...always saying minus does leave a sour note in our wishing it to be milder. Like last winter, it didn't start until mid January...I was golfing on this date last year....shot a respectible 85. I think eventually the U.S. will join the rest of the world by using the metric system. It does in most scientific and manufacturing processes....only in temperatures does it hang on to the old ways. And you too can learn to appreciate + numbers.

It can be useful to use a bulb basket for planting out if you have a small garden. It's a bit easier to locate the plastic container and reduce the risk of bulb kebabs on your garden fork...:-((. Then you can clear away the bulbs in time to plant up for a summer's display and watering regime. If you want to do this - be sure that the pots you use have very generous holes otherwise the daffs particularly will circle the pot many times before they find an exit. Not optimum for developing buds and reserves for the following year. Also - some Narcissus seem to be downright picky about flowering in pots more than once. (Jonquils. Tazetta.) Others, such as Tete a tete and Jetfire are quite uninhibited and multiply generously. The system you're proposing - lift and replant annually - definitely works in my zone. Make sure you select your bulbs for size and keep the smaller bulbs together for growing on. Tulips. Deep pots are better, IMO. They provide enough room for the droppers and the formation of the new bulbs. But I'd have to be very fond of the variety before I'd be excavating foot-deep holes.

I think you might have trouble in the shed. Most spring bulbs originate from areas where the ground never actually freezes in winter, and here they recommend planting them extra deep, I presume because of our cold temperatures. I have done pots of crocus and small daffodils successfully, but that was kind of underground... we had a sprinkler system, and the controller for it was about a foot below ground level, up against the house, in a dug-out box where you lifted a wooden panel to gain access. So I put the potted bulbs in there, and covered it with the wooden panel, then let the snow mound over that naturally. Then in February or so I would bring the pots indoors for a pre-spring treat. Another method that has worked for me is to put pots of crocus bulbs in the back of the fridge, but that obviously cuts into food storage so isn't ideal.

We can't answer this without knowing what your outdoor temperatures are compared with temps in the garage. Tulips are not fazed by freezing temps but if they have been in a much warmer environment they will need hardening off. btw there us a Bulbs forum. This isn't really Winter Sowing as such.