Jace:
Mount Baldy is a popular area for people to learn ice axe & crampon use. You might want to head over to the
San Gabriel Mountains Discussion Forum and get to know some of the guys there. TacoDelRio, the site admin is pretty heavy into winter climbing, as are several others there.
There is also the Sierra Club's
Wilderness Travel Course. They no longer teach ice axe and crampon skills because of liability issues, but they will cover basic snow travel, basic avalanche awarness, and they will take you on a snow shoe backpacking trip. The course covers backcountry travel pretty much from A to Z, including sections on first aid and navigation. They also will make available discounts for gear purchase and discouns for mountaineering courses that do teach ice axe/crampons. It's a really good course; I highly recommend it. If nothing else, you'll make a lot of connections
There are professional courses available. A professional course might be expensive (it will), but people
die when they use 'pons & axe and don't know what they're doing. A couple of us here on the forum have personally lost friends/family due to winter ice accidents. Nothing to screw around with.
Kurt Wedberg, who some of us here know or have met, has a school,
Sierra Mountaineering International (SMI) that offers Snow Travel courses. An avalanche course might not be such a bad idea either. Kurt has climbed Everest more than once.
HJ
P.S. Hope I don't sound like your mom here.

Plenty of people do winter climbing and stuff just fine. Just use your head, and I'm sure you'll be fine.