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yes it is still alive, roses are pretty tough. here's a few pointers
Make sure that window box planter has a good amount of drainage holes on the bottom.
Don't let the soil dry out, water when the top of the soil feels almost dry then give the plant a good deep in watering
Give it as much sun as possible and just let it wake up. when it begins to have a couple of sets of leaves emerge you can give the plant halve doses of fertilizer. but mainly don't stress to much, there seems to be some green stem left and the worst of winter is passed. give the plant plenty for sun don't let the pot dry out and six weeks from now the plant will be growing like a weed. Also, after it wakes up whatever looks dead you can prune off.

I'm not sure a 6 inch deep pot will be big enough for any length of time but you can start them out in that. As they get larger you may need to go up in pot size.

That looks like cold weather die back on the tops of those canes. I don't know where you are but in my zone 6 it's way too soon for them to start growing. In a normal year I would have started pruning but it's just been too cold this year. I do see some nice fat buds on the bottom of those canes.

Yes, lots of drainage is important. Roses hate to sit in water. Prune off all of the dead wood. If you don't it will continue to die back. Be patient. When it really does start to warm up they should take off.

Just prune the dead canes and let only the greener part be there. Water + sunlight + patience is what you'll need to get back this rose.

The roses will surely live back and bloom big babies !

Those roses are on their last legs. I don't think there is very much hope. You have cane die back, but if you cut off all the brown parts, you won't have almost any cane left, but you have to cut off the brown parts. If I am wrong and they recovered let me know. I just added coffee bean.

Yes, it looks really great. It had some rust but it responded will to treatment.