Look forward to your pic. When I imagine a larger space I had different thoughts than when I considered it might be a smaller portable-type thing...

One corner (house is to the right): {{gwi:4345}}
Wall opposite house where i want to place vines or some big plants:
{{gwi:4346}}

Sunroom is 12X12

very nice! so which way it's facing? south? if it's too cold in winter you could winterise: tape 'big bubble' plastic sheeting all around. yah, it's not cheap, but probably less then supplementing heat. you could put a couple of baseboard electric heaters too - that proly will be even more expensive, but you only need to run them at nite for a few hours. during the day it will heat up a lot when there is sun - i expect to high 70s and even 80s if it faces south.
some simple sturdy unkillables for wide swing of temps would be spider plants, ivies, jades, calamondin orange and may be other citrus, some bromeliads (need to be shaded somewhat), cacti too. provided your temps don't go below 40F. most of the above can take even lower , but best not below 34-35F and not for more then a few hours. keep succulents/cacti on the dry side then. check the florida forum for winter gardening - that would be close to your conditions : hot and sunny during the day and dropping low at nite. especially look at posts about frost advisories to see which subtropicals pull thru.

It's facing west.
I don't want to tape any kind of sheeting because it will not look nice from our living room.
I'll check Florida forum. thank you

also search for 'unheated sunroom' and 'unheated porch'. i found some interesting tips on gardenweb: heat cable (used to keep the ice from building up on the roof of the house). Just run it around the inside base of the greenhose and plug it in at night.
as far as plants: nandina domestica resembles bamboo and looks like a small tree, it is happy in the pot, slow growing, withstands low temps well - you're in z7, right? - so it probably will not drop any leaves even if it gets cold.
look into camellias (bushy, evegreen) and also 'winter jasmine'(evegreen vine). these are all plants that winter outdoors in z7b, but of course in the pot they need more warmth.

Wow that's a NICE, big room! Sweet.

That looks like you could grow about anything you want in there with a small amount of supplemental heat at night. We heat our whole house on cold nights with a couple electric heaters that look like old-school radiators. They're filled with oil, which retains heat well, and heats up easily, very inexpensive to run. I think some kind of risers or stands would be helpful also, to keep the pots from contacting the cold floor. If you could find some black plastic tubs and fill them with water, they could serve as stands and absorb heat which they would retain for hours after nightfall. Put away for summer when it warms back up. It should be fairly easy and inexpensive to prevent frost in there on cold nights.

I love the suggestions above, and would add Gardenia, Rosemary, Basil, ornamental sweet potato vines like 'Margarita' and 'Blackie.' What about house plant type vines, like Pothos, Philodendron? Hardy ornamentals like Tradescantia zebrina & pallida, Gibasis geniculata (Tahitian bridal veil.) If these last did get frosted (but not frozen solid,) they would grow back.

Are you able to open some windows out there when it gets too hot?

thank you, Petrushka and purpleinopp for your ideas.
Now i have something to think about.
I can open all windows and there is sliding door as well, when it very hot, I open door or windows. Heat is not a problem (well not on very hot summer days).
I like my dream sunroom and want to make it very greeny.

one more came to my mind: norfolk isle pine. it likes 50-70F range , but 40s are ok. and it's easy to get it before xmas - they sell it as indoor xmas tree. they say what they sell is really 'cook island pine' (needles point down) but it's marketed as NIP (needles up). it's araucaria columnaris. but it does not like frost. so it all depends on nite conditions in your sunroom. usually closest to the wall center is the warmest spot; corners are coldest and next to windows of course. the difference in temps might be 2-5F.

I like it too, and dream about having such a space. The biggest problem you might have getting started at this time of year is that the selection of plants available to buy will be pretty slim until spring. It will be a learning experience for you, and hope you'll have some updates to share!

What temperature does it actually go down to? That will give us an idea for suggestions you could try. I'm wondering about citrus. Also other scented plants like Jasminum polyanthum, Hoya carnosa etc. Also a perfect place for winter flowers like cyclamen, hyacinths, paperwhites, azaleas, etc. which dislike the heat of the house.

Roof blinds would control the heat in summer and help retain heat in winter.

I have rosemary and camellias on my balcony now and only just moved my savory, oregano, and aloe plants inside when the temps (finally!) dipped below freezing this week. You could also do potted lavenders such as Goodwin Creek or Dwarf Munstead. I'm overwintering a bare fig tree out there too but it's not very pretty. I know bonsai can be easy to kill (personal experience!) but some types like the evergreen junipers like to go dormant outside. You're lucky to have such a nice space!

OK, well I have an evergreen vine suggestion-- a hardy confederate jasmine is evergreen (Trachelospermum jasminoides). Mine is living outside, but has stayed nicely green all winter.

Thank you, Lizza and Julianna for good ideas.
I'll check your suggestions.

My guess is, that what goes around the southern France, Italy or Greece, will also go in that space. Hot summers and cold, but still rather mild winters. Stuff like Bourgonvilla might die down in the winter, but would perk right back up, in the spring! Stuff that goes outside, but has a short blooming period out there, might get a longer period inside (how does the smell of moonflowers from early July to mid November sound to you?). Eucalyptus might die down the first couple of winters, but will in time get very strong and tall. I think a bay-leaf would do well year round. Peaches and grapevines would do great as well, no doubt about that. Figs too.
Passiflora actinia and caerulea plus some of the hybrids can withstand down to -8c/ 18f.
I÷m envious!

My guess is, that what goes around the southern France, Italy or Greece, will also go in that space. Hot summers and cold, but still rather mild winters. Stuff like Bourgonvilla might die down in the winter, but would perk right back up, in the spring! Stuff that goes outside, but has a late blooming period out there, might get a longer period inside (how does the smell of moonflowers from early July and onwards sound to you?). Eucalyptus might die down the first couple of years, but will in time get very strong and tall. I think a bay-leaf would do well year round. Peaches and grapevines would do great as well, no doubt about that. Figs too.
I÷m envious!

Now that÷s weird... an earlier version of the above post, was posted AFTER I posted the finished one... Go by the first one..
BTW, the passifloras will probably also die back in the winter, but would shoot back with lightening speed in spring.... and begin blooming very early, and continue even after beginning to set fruit!