the "batwing" saloon doors did exist, but they weren't quite as hollwood westerns depict.

for one, they were usually much larger than in the movies (big enough that they could be locked after hours to keep out intruders). in ronald james' "virginia city: secrets of a western past" he argues that movie producers made the doors smaller in order to make leading men appear taller.

they were also not as ubiquitous as in hollywood westerns. james argues that these cafe-style doors were preferred because they A) made it easy for people carrying large parcels to enter hands-free (you couldn't leave your stuff outside on your horse or it might get stolen) and B) shielded church-folks from having to see the drinking, whoring and opium-smoking going on inside (many saloons also functioned as opium dens).

but these doors would be impractical in northern climates and as such, they would not have been used.