Part of the supposed strategy also involved hitting Ukraine when Europe is reliant upon Russian gas for heating. I was a bit surprised how late into winter they invaded given this goal.
I read a few days ago that Germany's gas reserves were at 31% and they were basically just being helped by the good weather. A colder winter would've made it a much bigger problem. And Germany had very recently decided to basically go cold turkey on nuclear, which means using more gas plants. Now they're thinking of extending the life span of nuclear a bit. Not that a gas furnace can heat with electricity though, so not sure how much that will help.
If you had to replace every single gas heating system that would be both very expensive and without having any actual data I would gather that you wouldn't be able to retrofit all of Germany with that in time. Wood I would gather is gonna be even worse. While I can see how a single family home would convert (lots of folks have replaced their gar furnace with a wood pellet heater w/ auto-feeders), how would that work for apartment buildings with individual gas heaters in the apartments? These are all concrete buildings where it'd be quite the feat to replace the gas distribution with central water distribution for radiators. And those gas heaters do not take a lot of space and are used even in tiny apartments. Where do you store wood pellets in that situation?
Of course there are exceptions where heat is provided remotely already by a "Heizkraftwerk" (e.g. fed from industrial cooling systems or garbage burners).