may not work with moose, but
The way I deal with squirrels (after much trial and error) is to just keep going in a straight line and not even try to avoid them. If I swerve to try to avoid one the little bugger just manages to dart right in front of me again anyhow, and by then I might be off balance enough so if I did hit him or try to swerve again I'd go kerplunk. So may as well keep the odds in my favor and stay on course, so far all they've done is play chicken with me and dart out of the way at the last moment. Haven't hit one yet, thank goodness ...
There was one day hubby and I were out riding and the squirrels were being especially aggressive. It was right after we watched one of the Pyrenees stages of the Tour on TV, so we started envisioning the crazy squirrels darting in front of us wearing little orange T-shirts shaking their little paws at us (w. some of the ruder ones flipping little squirrel birds at us) squeaking their tirades as we navigated through the rowdy crowd ... hey, it was a funny visual :D