Gloves for wet riding

Have much luck with your gloves/mittens when riding in the rain? Got
truly waterproof gloves? How do you dry your gloves when they get
soaked inside?

It was pouring last week when we were at Sierra-at-Tahoe. Snowing at
the top. Anyway my daughter & I use our Gordini gloves that usually
seem reasonably warm. Mine are Goretex/Primaloft, hers Drimax/Hollofil
II. Anyway they both got soaked through. Less warm when soaked, and by
the afternoon we avoided higher elevations to keep our hands warmer.

Another problem is they won't dry. We used to use REI gloves, and we'd
invert their liners when we were done. These gloves don't seem to want
to do that, and it seemed to mess up the REI gloves after awhile.
After several days of hanging up to dry, I turned most of my gloves
inside out, and it was able to squeeze quite a bit more water out. Not
enough for it to dry though.

We tried using a hair dryer on "cool" to dry the gloves, but the hair
dryer quit.

Help!