For Gorgonio, good lug sole boots (waterproof is great!), spikes, snowshoes if fresh snow or off trail, crampons/ice axe can be useful esp if going up high.
When I winter hike, I wear my thermo leggings under hiking pants (if temps in high 30s/40s) or under some Patagonia lightweight but warm winter waterproof lined pants for the colder days. I always bring my puffy and just got an awesome Arc’tyrex shell, plus a baclava and thin gloves plus warm mittens as my hands get cold. I wear warmer socks too and bring snow gaiters if snow deeper and put snow baskets on my poles.
Keep in mind you generate heat going uphill so pack layers. Snow hiking goes slower too, so consider this when planning your route. For me snow hiking I focus more on time than a destination like I do in non-snow conditions.
Happy hiking! Snow is so pretty! Did Deer Springs up to part of PCT other day and snow was really great there too and beautiful views!