The solution is to dig up and divide the crowded clumps every four years or so, in the fall. Take the opportunity to dig in some fresh low-nitrogen fertilizer, such as bone meal. Replant the bulbs growing at the edges of the clump, one to two feet apart, and discard the old bulbs from the center. A healthy vigorous rose is much more likely to get through the winter unscathed than is a stressed or diseased plant. Sudden changes in temperature in the fall, before the plant has had a chance to harden off for the winter can be disastrous.
Early freezes kill more canes than much colder winter freezes.
Most hybrid teas that are reasonable hardy for the site can be adequately protected by mounding 8 to 10 inches of loose soil or compost over the root zone. Prune the rose only enough to prevent wind or snow damage. If the winter weather is dry the rose will need to be watered every three weeks or so. Be careful not to remove the protection too early in the spring.