Hi and welcome, Ziya!

You may have made things harder on yourself as far as pruning goes by weaving those branches into the trellis. It's always much easier if you don't weave but just tie the branches to the trellis. Then if necessary they can be released from the trellis to prune or what ever. Trellises also tend to weather and need replacement from time to time. If the rose is woven into it replacement becomes a real problem and you have to whack it off to get the trellis out. In the future just fasten the canes to the outside instead of weaving them in. You can use twist ties, twine or what ever you wish that can be tied and then released when necessary.

How much you will need to prune it back will depend on how severe your winter is. In zone 6 sometimes we have nice easy ones and a lot of the cane will live. Other years you may need to whack it all off in the spring. In the spring when they start to wake up (for me that's usually early April but could be different for you) you should be able to tell what is healthy cane and what is not. Anything that is plump and green should be OK. Any cane that is brown/black or withered/shriveled will be dead. Also cane that has black streaks down it is usually not going to stay viable for long. But one caution here, as older canes age at the bottom they will become brown and barky looking but they are still alive. A good way to start out is to go to the tip of the cane and cut off about 2 inches and look at the center of the cane. If it is white/creamy/greenish it's alive. If it is black/brown/tan it's dead wood. Keep cutting off short pieces until you reach a section that has that white/creamy/greenish center. With practice you'll get to know what is and isn't still alive. Don't worry if you accidentally take off something that's still good. It happens to all of us all the time, lol. It will grow back!

I do think your container will be too small. I put a single mini, and not a climber at that, into a pot that size. Climbers need to have larger root balls in order to be able to send water and nutrients all the way up those long canes. If you can get another one of those containers you might want to put each plant in their own pot.

As for the blooming, my first thought is are they getting enough sun. Lack of sunlight is a major reason why some roses don't bloom. Roses need at least six, and prefer 8, hours of full sun to bloom their best. And feed them. Roses are pretty heavy feeders so fertilizing them may help to keep them blooming more.

Looking forward to hearing more about your roses next spring!

Try doing what Seil says, especially concerning the size of pot. I've been told Cl. Rainbows End takes a good 3 yrs to really start producing lots of blooms.

Thank you Seil, I was hoping you (or another GW expert)would respond on this...I've been reading forums to make it thru the winter and learning so much. Sounds like my best bet on this may be to give the Rainbow's Ends a totally new pot and something to climb in the spring. I have a 10 gallon urn that may work once I figure out something for climbing...I think I will like the fancy trellis pot more for annual vines anyway. Hope I won't have to cut off too much to get it out of the trellis. I had also read these roses can take more than a year to bloom happily, even with extra food and LOTS of full sun (at least 10 hours). I like the idea of tying the branches, seems less pokey (my new leather rose gloves should also help). Thanks for the advice on pruning, this is a source of worry for me as a new rose grower but your description made me think of The Secret Garden. We are having a harsh winter for KC, so I'm glad the potted miniatures (Rainbow's End, Black Jade and about 15 tiny grocery store minis my sister "rescued") are protected in the garage. Hope the 3 Buck roses in the ground (Quietness, Distant Drums and Wild Ginger) live up to their reputation for hardiness!

I grow Jean Lajoie which is a beautiful pink. It grows in a corner of the fence and I don't do anything with it and I have hundreds of blooms on it. Miniature are all hardy and will stand the cold.
A lot of roses when first planted should not be allowed to bloom. Why? Grow roots, then leaves and then blooms.

A quick update. In april I untwined all the canes and then after looking at it for awhile I decided to plant it in the ground in my backyard (with a big trellis and small shed to cover, if it's happy). It didn't like the move much but seems to be recovering nicely. I think my sister is rooting for it to die so she can plant a Cl. Joseph's Coat in that spot...I can't yet bring myself to kill a healthy rose, not even the 2 double Knockouts that were my first ever rose purchase (before I knew anything at all LOL).

Glad to hear it's doing well! Pictures?

Sadly (or not, depending on your point of view) the Cl. Rainbow's End didn't make it through the summer. Possibly for the best as we are looking to buy our first house before next spring and I am already unsure how many roses I'll be able to move, This house will go back to being a regular rental, so little point in leaving much in the ground.