We just purchased a house and been using the washer for two weeks. Now suddenly the floor drain near by has quite a bit of water coming up out of it during the last spin of its cycle. Also, toilet near by has soap bubbles during wash. Could it be from roots in the line. It's been very cold.

I don't know know if it's roots but you definitely have a partial blockage downstream from the floor drain. Are you on a sewer or septic tank?
Let me know, Tom

Sewer. I'm curious why it worked fine for two weeks and now suddenly its backing up. Is this common?

Sewer. I'm curious why it worked fine for two weeks and now suddenly its backing up. Is this common?
Clogs and blockages are unpredictable. Yours sounds like it's out in the sewer line . I say this because it took the washer pump discharging twice before you got a back up. Washer pumps discharge with great force and much volume in a short time.
If anything's going to back up it will be caused by the washer discharging a load.
I would have the sewer snaked paying special attention to the street raiser connection to your sewer. In the past we have had a root problem at that point. Good luck, tom