As you probably already know it is highly unlikely a deer or elk would attack, but in the one in a million chance one would (has happened I know). Then Bear spray or mace which is an irritant would just as likely cause them discomfort and to disengage an attack as it would a bear or person that was attacking. Nother words I don't think they'd like it.
Did Trigger attack and you had to use your bear spray? Sorry, I couldn't resist. I would think it would work on deer or elk but who really knows. As mentioned before, it is an irritant and should effect any animal.
I work with horses for a living and it will and does effect horses . It will not necessarily effect their skin but if sprayed in their face wear it is hitting more sensitive like the membranes around the eyes mouth or nostrils it would work. A few years ago in yellowstone a ranger was attacked by a cow elk around Mommouth springs . She had a calf with her and she charged him and knocked him off his bike. He turned his bear defense on it and it turned the cow away .
There is one tip I have learned over the years in hunting whitetails in late season snow. Do not overlook soybeans left standing on the edges of fence rows, woods, creeks, buildings wherever it might be, this is where the deer will be while the food lasts during late season. December/January will pull deer in from some distance away to feed on the easy to get to food.
I killed one of my nicest bucks off of a very small patch of soybeans that was left after rains created a...