Yes, most roses do go dormant in the winter, and winter is normally
the best time to prune. I'm not sure what your frost dates are, but
try to prune after the last hard frost, so you can see what all the
dieback will be, but before the new shoots come out. You can take out
deadwood or rubbing limbs anytime. If you're starting from a
long-neglected rose garden, pruning all of them down to six inches
above the ground might be a good idea.

Most modern roses bloom on new wood that they grow out every year.
Some old roses bloom on wood that's been out for a year, so if you
take out all the old wood they might not bloom that summer.

Prune your slow-growing rose too. Pruning it might wake it up to grow
more.

If after a year or two your large-growing rose is still way too big
there, think about moving it or replacing it. Trying to force a big
rose to be small is just going to frusterate both of you.

-- Patrick