One of the small plants I like growing are cold hardy succulents like sempervivums and sedums because they look kind of unique and are completely hardy in zone 6. Some of the bigger sempervivum varieties are prone to getting eaten by deer, but it depends on their color and where they are planted. Planting them closer to objects like a house, bricks, or deer repellant plants can keep them away.
Sempervivums also known as hens and chicks usually start growing in the winter as long as the soil is not frozen and continue growing until the summer when the soil dries up, generally producing offsets by around May and they go dormant in the summer when the soil is too dry for them to grow. They will just sit there until around October when the soil becomes moist again, and they get a bit bigger since these are cold weather plants.
Here are some of them from my huge collection
If they produce chicks, I will often pull them off and plant them a bit farther away from the mother because at this size, they will all likely produce their own offsets.
So many of these species look almost identical so I don't bother with identifying their names. I have them planted a good distance apart and just hope I don't end up one dominating species eventually take over.
Sedums: These proliferate way faster than the sempervivum, and they produce seeds that germinate nearby as well so these will basically survive in a lawn as long as the grass is removed. They grow low enough to the lawn to avoid getting cut up.
Last fall, I took many pieces of sedum to spread them out more so they can cover ground faster, and a little piece of sedum can produce a nice clump of plants in a single season since they basically grow year round with the exception of summer.