slow draining bathtub - is a frozen pipe a possibility?
It seems pretty unlikely that the drainpipe would freeze in your crawlspace.  Even if there was a 20 degree wind whipping through it (which there isn't: it's enclosed), the only way that could be is if there was standing water in the pipe to freeze.  That would mean a trap in the crawlspace which would be highly unusual.  And if you really had a frozen pipe, it wouldn't drain at all.

Most likely you have a hairball in the drain. Try a "drain zipper" and/or a drain auger.  When buying a hand auger, it's worth it to pay more for one with a toggle lock as opposed to a thumb screw.  It will save you a ton of time and your hands will thank you.