I would never trust so vital a navigation instrument as a compass to anything requiring batteries, and especially not to something as difficult to use (those tiny buttons are hard to push and don't always work) or as prone to malfunction as a wrist watch. My Silva Starter Compass, which I've found quite adequate for navigation, even off-trail, weighs 0.8 oz., costs under $10, and is carried on a cord around my neck, along with my whistle and Photon microlight. It's a basic compass, but does have a (short) ruler and adjustment for declination.

I dont take an altimeter/barometer since I can get the approximate altitude from the detailed contour map(s) I always carry. I've learned to read weather signs, so my prediction success has been pretty accurate. If I wanted one, I'd get one that was more durable and easier to use than a wrist watch, or I'd go whole hog and get a regular GPS (not the wrist watch kind). Again, even if you get one of those fancy watches or a GPS, you still should have the manual compass.

In 70 years of backpacking, I've never felt the need of a thermometer. If there's ice in my water bottle in the morning, I know it has been below freezing. The one time I deided to take a zipper pull thermometer. it got down to 15* F. The only thing that knowledge did was to make me feel colder!