Expect winter or spring conditions; March 13 - 19 is not that late in the season. I've skied Tahoe the second week of April and had new snow and freezing temps one day and summer temps two days later. (When it snows in the Tahoe area it snows; accumulations are measured in feet rather than inches.) Even during the warm days, you'll generally encounter cool temps and firm snow higher up the mountains.
Don't waste too much time by frequently traversing back and forth between the Nevada and California sides of Heavenly. There are some amazing views of the lake from the traverses between the two sides, so don't avoid them entirely.
The ski area with the best views from the lake is a small local's area called Homewood. It's maybe a half hour drive from Heavenly (on the California side.) Homewood is worth trying on a weekend to avoid the crowds; it has a trailer as a lodge so expect zero ammenities there. Only go there if it's a sunny day.
If you ski off the groomed runs, you'll find out why the snow out there is called Sierra Cement. Especially if it's been warm and/or if you are skiing a face which gets a lot of sun. You won't notice the difference on the groomed runs.
If you get lucky at the casinos, you may end up with a free vacation.
Or you may end up paying for two vacations.