Not a good idea; painting will activate the glue on the wallpaper and it will start to peel.
Don't, just please do not do this. I know people that do and then they seriously regret it. Much harder to remove wallpaper after it has been painted.
To remove the wallpaper, score with "paper tiger" using slight pressure - don't press hard enough to dig into the wall behind the paper.
In a spray bottle mix warm water & either white vinegar or fabric softener (50/50). I use fabric softener because of the smell.
Saturate and as it gets into the holes, the glue will "melt".
Scrape with a plastic scraper.
Wipe walls down with warm soapy water with blue Dawn.
Thank you. I keep seeing that this is the ONLY way to remove wallpaper. However, I was told to prime with oil based primer over the paper then in a couple days paint it. I'm not that stupid. I know the paper will get worse and more difficult to remove. So for now, I think waiting until I can have the windows open and it not be 12 degrees is the best idea for me. Thank you