How do I fix seams that open up at the corners of walls during the winter?
The reason why this is happening is the structural members are expanding and contracting with the temperature/humidity changes.

There is no good solution to fix the issues, but you can cover it up.

The quick and dirty solution would be to put up quarter round over the seams, and attach it to the studs only- That is not to the ceiling.  This would allow for the expansion/contraction to remain covered.

Other options would be to install Cove moulding.  



or Crown Moulding



Note that the Crown shown here is clip on, and the clip attaches to the wall only.  Again, this allows for expansion.

These can all be DIY projects if you're comfortable with finicky work.  It's a bit tricky to get the corner mitres looking nice and tight, and you'll need a compound mitre saw.