I've lived in that area for eight years and during that time either up to Lake Tahoe or to Silicon Valley in pretty much all weathers. I've got some opinions .
First, the Mazda 3 is FWD, right? In that case, no matter what tires you have on it, your son will need snow chains (and know how to use them). Without chains, CalTrans will not let him across Donner Pass or Echo Summit during a proper snow storm with chain controls. I've not seen them check that much on CA 88, but if both Echo Summit and Donner Pass have chain controls, you'd have to a have a bit of a death wish to use 88 without appropriate equipment as that's the highest pass of the three.
NHP at least IME doesn't care that much, they just write you a ticket after they found you and your car in a ditch. The only exception to these rules is if you have AWD and full on snow tires.
In Reno and the Carson Valley, you can usually get away with All Season with good snow capabilities and chains. If your son ventures into the mountains, he will want proper, full on snow tires, not 3.5 season ones. Blizzaks are his friends in that case.
All that said, the area generally gets snowstorms a few times each winter. It's not like it's dumping down snow there for weeks on end - you get potentially really nasty snowstorms that last a couple of days. I'd generally recommend just staying away from the mountains during those storms unless you absolutely, positively have to travel. Reno has a perfectly functioning airport for when you have to .
The issue isn't necessarily so much the snow, but you might get stuck in traffic on the passes for hours, either because of accidents or because they're holding traffic. Also, there are a couple of lesser known, lesser traveled passes North of Reno that are much lower elevation and thus often open and less dangerous than the main passes. Those are no joke either, but I've used them as detours when I had to because the other passes were closed.
Now, back to tires. If you want some local advice and tire recommendations, I can recommend these people: http://www.inclinetire.com
They're definitely not the cheapest, but they are one of the best if not the best tire shop in that area. They'll even store the seasonal tires for you if you decide that you want to go with two sets. If you talk to the owners (Cate, unfortunately I can't remember her other half's name) tell them Timo sent you, they may remember me.