We use hay or mulch out here, too-but we put it over the soil around the plants in the curbed gardens to keep moisture in and invasive plants out-cuts down on the time spent raking out weeds. I also use landscape fabric-it is cheap and effective.
Mulch is cheaper than hay here-it is sold for less than $20.00 the pickup load at the fire station. Hay is needed as feed for livestock, so it is more costly.
If we weren’t in a neighborhood I would love to just have a sparse yard with native plants. I always smile thinking of the deer eating away at plants just outside your yard. Was it you saying they eat wreaths and fall displays if they have corn or something on them?