The latest snow depth map I found shows only a few inches deep in the Horse Meadow area, getting to 12-18 inches deep by South Fork Meadow. Above there you can expect the snow/ice to be more significant. I recommend microspikes (at least) up to the meadows trail fork and then above there I’d suggest that you be prepared to put on crampons to deal with the thicker ice. Snowshoes may be useful somewhere in the 9,000 foot level and above.
So far just going by local knowledge and seasonal reports up to late March to guide me. If you decide to go, first be safe (of course) and second I can use first hand reports and would appreciate anything you can share about the conditions.
Hope that helps