In March, unless it nears Easter week or is an exceptionally nice weekend, campsites should not be hard to get either at Camp 4 or the others eeek mentioned. This page
http://www.nps.gov/yose/planyourvisit/feesandreservations.htmshould link to any info you need. If you plan for Upper Pines, you should get reservations, at least if you're staying the last half of March. Wawona should be on 'first come, first served' at that time, but check the website.
(note that Camp 4 is a site that can be packed in up to 5 tents (of their choice) per campsite, and may not be to everyone's liking...or you may think it's great)
For the first half of March, you can make Upper Pines reservations starting October 15 (if they are doing reservations for that time...it varies from year to year). For after March 15, you'll need to make them November 15, and if it happens to be near Easter, I'd suggest doing it that day, early. The conditions there vary...it's a great location, but on a busy week you're definitely going to have some larger or rental motorhomes there. Wawona is a nice alternative and usually uncrowded in winter.
The need for snowshoes depends on what altitudes you're heading into, and just how "recreational" your fiance's are. There are lots of places to go on snowshoes from the Badger Pass/Glacier Point area, and Merced Grove is beautiful when it has fresh snow. (March is a big question mark as to conditions there, and how useful snowshoes will be). If she likes them, and they're sturdy enough to not come apart, they probably are fine for those areas. Both of those areas are highly recommended for winter snow walks. I believe you can also camp in the country near Merced Grove if you're wanting to snow camp, but you need the wilderness permit.
The only trail out of the valley that's usually open then is the upper Yosemite Falls trail, and you will possibly need showshoes if you plan to walk around the top...but be careful, as it's not so easy to find your way around up there in fresh snow, and there are hazardous areas, even on the last part of the trail up.
Gary
Yosemite Photo Galleries: http://www.pbase.com/roberthouse/yo