I'm finding mixed answers to this question across the web, so I'm hoping someone can respond with personal experience.
I do have personal experience, and it depends on snowcover and available food. Phlox subulata is not known to be deer resistant, so if it's an "open" winter and more tasty food is not available, the deer will browse the phlox but they probably won't kill it (they never killed mine). I've never seen deer dig it out from under snow, though, so if you're in a snowy climate you'll be fine. I've also never seen deer go after it during the summer - but again, that depends on other available food.
When I lived in a rural area, I had pretty good success planting sacrificial plants in my woods, well away from the house - things like daylilies (NOT Hemerocallis fulva - "ditchlily" - which would spread, but ugly seedlings of my own) and the old-fashioned plain green and green-and-white hosta, which I got free from a neighbor. The deer went after these instead of my garden. I also noticed where the deer wandered into the yard and made paths for them (and me, of course) that skirted the house (sacrificial plants planted near the paths). Deer seem to be lazy critters and would rather follow a path than wander through undergrowth.
If sacrifical plants and paths aren't feasible, and you don't have snowy winters, then you're really at their mercy. Individual deer seem to have favorite plants, but their rule of thumb seems to be: 1. Eat the most expensive plant in the yard, followed by... 2. Eat the gardener's favorite plants, followed by... 3. Eat everything that's not native to their habitat, in order by price, followed by.. 4. Eat everything else that seems tasty and not poisonous.
If deer are a severe nuisance, you can always make a garden from poisonous plants (hellebores, daffodils, lilies of the valley, baneberry, bearded iris, aconitum, etc.).