More important in winter than means of transport is logistics. You better always have a heated hut and better not operate far away from such necessities.


Military bicycles appeared in army exercises in the late 19th century, especially folding bikes are quite well-documented (as if carrying a 25+ kg bike on the back was somehow an advantage). It's difficult to pin down the first wide-spread use to me, and it surely wasn't a primarily defensive tactic in German use.
Germans used bicycle troops mostly as cheap cavalry and motorcycle infantry substitute, for example in the battalion plus-sized reconnaissance detachments.