Prune out dead leaves and petals from the plant. However, do not prune the half alive ones because taking off will signal the plant to start growing again which you do not want during the winters.
You need to supply the plant enough food to go through the cold. Give it one last shot of fertilizer. However, the fertilizer that you choose should have a lower nitrogen content because nitrogen spurs growth.
It is advised to keep the rose pot outside till the first frost. This way the rose will feel the chill and go dormant. If you shift it indoors earlier, it will keep growing through the winters.
After the first frost wave, move the pot inside to a garage or anywhere with shelter. The place needs to be dry and protected from wind. A covered yard or shed will also do.
Store rose pot:
In the sheltered location, snip off all the leaves and flowers from the plant. When left on, these cause diseases. Remove all these and debris from the pot to prevent any mold. To protect the roots, you can cover the pot with burlap sack. Water a little once a month through the winter. This will keep the roots hydrated. Do not over water because the roots can rot in dormancy.