It is okay to look at the weather report and rearrange your riding calendar to put the long rides on the nicer-weather days. Ask your coach for help.
Ride outdoors as much as you can, even if there is a bit of rain. If you ride in the rain, dress so warmly that you’ll still be warm when you are wet and that you will actually be relieved to get wet.
Studded MTB tires on ice have grip as good or better than regular road tired on pavement. If you really have ice to deal with, get a set of studded tires. They can be had for less than the cost of good road tires and you can use them season after season if you dry them and store them in an airtight bag in the dark once the ice has all melted.
When you get home from a winter ride and you are cold, the fastest way to warm up is to strip off the wet clothes and jump on the trainer. You can generate heat internally much more effectively than you can absorb heat from food or a shower.