Well, I don't know how you're going to see any snow if you stay on the coast. I don't think there's any snow there at any point in the year, let alone as late as late April.
Lucky though as far as driving goes there are not many options you're going to need to rifle through. Assuming you're starting in
San Diego, take I-5 to
Los Angeles. This ~100ish mile route hugs the coastline which should be in tremendous shape by the time you see it. You'll go through Del Mar, Oceanside, and Capistrano Beach. Then you'll head inland as you near LA. Once you hit LA start looking for US 101 signs, and get on that highway.
Take 101 all the way through Gaviota State Park. At the end you'll be able to get on CA-1, which you'll take ALL THE WAY to
San Francisco. Most of this route hugs the coast as close as you can imagine.
CA-1 and 101 share the
Golden Gate Bridge, but after getting off that you're going to want to leave CA-1 behind as it veers west to the coast and Napa is to northeast of SF. At this point I'm sure you can find directions from SF to Napa, so I won't go into further detail.
But that's pretty much the only route I can recommend. If instead you're starting at Napa then just reverse my directions ;) Good luck and enjoy the views!