Although dead and dying wood can be good for wildlife (bird nesting cavities, for instance), for the health of the tree, it's always recommended to remove dead wood promptly (any time of year) so any damage does not progress into healthy wood or cause more damage once it snaps off. You may not want to wait until spring because, as you noted, winter weather may result in it breaking off, which may take healthy growth with it, or create a jagged break that will not be easy to "clean up" with further sawing. The young growth at the base will eventually mature into replacement trunks (although at some point they would probably need to be thinned out so they don't crowd each other too much). Another reason to trim now versus waiting is that, if a bird were to nest in the cavity (and some species might by early spring), it would not be legal to disturb an active nest, so you'd need to wait to remove that wood until later in the year.

Miri