From the Tram Station to Round Valley Campground is almost 3 miles. A little further to Tramarack Valley Campground. Trail is somewhat up and down, elevation gain is 600 feet. The trail tends to be hard packed and slippery in winter. Unless there has been recent snow, the snow pack is usually pretty hard unless it is warm in the afternoon. You will be traveling at elevations from 8,500 - 9,100 feet. This is a good first winter outing. I would not be too ambitious for a first trip, especially if you live at lower elevation. You will be starting your hike at 8,500 feet.
You could hike from the tram to Little Round Valley, but you will be climbing up near the peak of San Jacinto, and 1.5 miles down the other side. A side trip to the peak is fun. Round trip is about 14 miles. However, you need to bring and know how to use an ice ax. Probably not a good first time trip.
For a first time multi-day trip you might want to set up a base camp at Round Valley or Tamarack Valley and do some day hiking.
I much prefer crampons over microspikes up there. Here are some weight specs for Kahtoola stuff:
Microspikes = 14.4 oz
Aluminum Crampons = 18.9 oz
Steel Crampons = 23.3 oz
I will take the 2 oz per foot penalty for aluminum crampons anytime. Note that rocks will dull the aluminum quickly if you choose to go that route.
Snowshoes are heavy and hard work, but sometimes needed. Often I bring snowshoes and crampons, hoping I don't need the snowshoes. I would rather carry them on my pack than on my feet :)
Footwear: You need warmer insulation and a means to keep your feet dry. You can use trail runners, but need a bigger size. My system is a liner sock, thicker wool socks, Rocky GoreTex Socks, Thinsulate sole inserts, and OR Verglas Gaiters.
You probably have warm enough clothes for hiking already, but need a puffy for when you stop or are in camp. Down pants are nice for around camp. as are down booties. Need at least two pair of wool glove liners as they can get wet. Also, it can get windy, so you need a shell glove.
Don't underestimate the weather. It can get very windy and the weatherman is not often accurate on possible snow. Take a 4 season tent if you have one. Lighter options are for people with a lot of winter experience. I have a Scarp 1 for winter only use in the San Jacintos.
A NeoAir is not going to hack it for most people. Plan on overnight lows in the 20's or even lower in winter. On June 1st last year, the high was 32. I use a Big Agnes Insulated Air Core and a thin foam pad.
A Tram ticket is $23.95 for adults. You can get a season pass for $150.
It is recommended you get a permit in advance if going on a weekend. A couple of Boy Scout Troops on a weekend can take up the quota. It is $5 per person.
If you would like some company, I would be happy to go with you on a weekend. All of my vacation days for the year have already been scheduled, so I cannot take any additional week days off. I live at the base of the mountain so it is easy for me to go if I have some advance notice to get a kitchen pass from the wife.