Someone had asked a couple of days ago about using a Dampit, and I found this video, which has very good information on humidity issues:

Short version:

Humidity: 40%-60%

Temperature: 65-80 F (18-27 C)

Avoid rapid, sizable changes of either temperature or humidity.

Wipe off fallen rosin with a clean (non-scratchy) cloth every once in a while.

Long version.

Rapid changes to either temperature or humidity are more of an issue than absolute amounts, although really high humidity (85%+) may cause issues with the glue.

As someone pointed out a few months ago (I think it was on this forum), wood has been known to survive thousands of years in desert environments. What will mess a violin up badly is going from normal humidity (in that 40%-60% range) to very low humidity (10%-15%, like Arizona in the summer) quickly.  If you stretched out the adaptation to, say, 15% humidity over a couple of years, it would probably be fine. You take your violin from a Miami beach on a muggy day and then fly to Arizona on a dry day, expect pain.

Cold is not much of a problem, but try to let the violin move to the colder temperature gradually. Easiest way to do that in most circumstances is leave it in the case until everything is at the new temperature. The humidity inside the case will rise as the temperature falls. I don't think most cases are airtight, but they definitely don't pass water vapor as fast as open air would.  If you know you're going to a significantly colder situation, loosen the strings a little. Cold will shrink them, which will raise the pitch and put more tension on everything. I'd suggest tuning it down about two whole notes. That's probably overkill, but it's still plenty of tension to keep the bridge and soundpost in place.

I'd try to avoid subfreezing temperatures. Wood is made of cells, and ice crystals forming inside them tends to rupture cells. Ruptured cells equals weakened wood.

Same thing in reverse when you're going from cold to normal. That would be a good time to put some kind of humidifier in the case with the violin.

Hot and muggy is something you want to avoid. That combination has been known to cause the glue to get soft, and people have had violins come apart in their hands. (Those were extreme cases, but it has happened, or so I've read.)  That's not necessarily a complete disaster (everything can be glued back together again), but it's probably something you want to avoid.

Rosin that stays on the violin for a long time (months) tends to sink into the varnish a little and won't come completely off. It doesn't hurt anything (as far as I know) except the looks.