Hubert,
Snowshoe hare follow a multi year cycle. Upland birds get hit harder during the low hare cycle. Where hare are plentiful, upland birds are found in better numbers. There will always be good pockets of small game density, that defy the cycle.

You not shooting a snow shoe hare will do nothing to the population cycle. The abundance and protection of raptors, they are way more effective than the humans and harder on small game.