My thought here is that rather than a pipe being frozen, it might be a vent. This observation already appeared in a comment, but I think that it deserves the visibility of an answer. Also, I have more to say than is covered in the comment.
As several people have noted, an ice clog is unlikely to cause a slow drain. This is because the warm water would tend to melt the clog. However, that's not true of a vent. A vent would typically be a pipe running from your trap up through the house to the roof. As such, the part that would freeze would be at the other end from where the warm/hot water is. Further, a blocked vent can be entirely obstructed and water will still flow slowly, which is the problem that you're having.
This question has photos of a piece of internal venting, an air admittance valve connected to a drum trap. I'm talking about external venting, which would look similar at the trap connection end but the other end is outside. You might be able to see the trap connection from the crawlspace. Or not. If you can't see the top of the trap from the crawlspace, then you might not be able to see the venting either.
Here is someone who was having problems with a frozen vent pipe. There are no answers, but a comment helpfully points to this question on unfreezing pipes.
If this is the problem, you should be able to see a pipe rising from above the bathtub in the attic (assuming you have one). You might try wrapping it with heat tape and seeing if that gives the external vent (on the roof) enough warmth to melt off. As always, be careful about mixing electricity (the heat tape) with moisture (the cold vent pipe).
Note: I'm not saying that this is definitely the problem that you're having, nor that other ideas are wrong. I'm saying that this is one possibility that may be worth considering, as it would explain the observed behavior without resorting to coincidence.
A problem with venting might also be caused by snow coverage (rather than ice). Perhaps the air is being blocked by an accumulation of snow. A house that I rented once would have plumbing issues if a vent was covered by leaves or snow. So the landlord would first clear off the vent if there was a draining issue. That vent was in the ground, several feet from the house. So if you can't find a vent coming from the bathtub trap, you might look around for other parts of the vent stack that might be blocked.