Grazing will absolutely effect wildlife on the property.
Sure, deer and moose will likely maintain a presence.
Though I wouldn't count on it. Seen it too many times where cattle have temporarily pushed big game to neighboring properties.
Odds are deer and moose use of this land would be much higher if cattle were not allowed to graze here.
Then there is all the small stuff most people ignore.
Birds, rodents and other small ones. Native plants.
Cows will definitely have an effect on the Wildlife. Depending on the grazing intensity and timing, the effect can be devastating. Yet many will not recognize the apocalypse before them, put up a picture of a cow and deer together and imagine that all is heavenly.
^ This should be enough to give your thread some traction.
Having said that, there can be positives to occasional high intensity grazing.
And Fire, and flood and drought. Nature sometimes needs a kick.
I would reflect on what this property means to you, what you want your role as Steward to be.