January is colder than December usually. We're not even over the peak. February should be roughly similar to December, March is when it gets better again usually. But that's still 2 months of people staying indoors a lot.
But the people I know kept to the private rules as much or as little as during the first lockdown, which seemed to work despite keeping public transport open. Which would enable similar transmissions as shops and schools.
if schools are open, it's pointless doing anything else. if schools are closed kids will still go out and play.
basically you're screwed if you do and screwed if you don't. and less and less people will listen as time goes on while the virus mutates and selects for contagious variants.