Yes, you can use magnum primers in handgun or pistol loads. They usually work best with medium to slow powders. But in sub freezing weather, they'll do fine with the faster powders.
Winchester's standard small pistol primer puts out more fire and heat than Federal's magnum small pistol one. Go figure. Prime some cases (no powder or bullet) and shoot them in the dark. See the difference between all sorts of primers. Most folks are surprised.
US Navy Distinguished Marksman Badge 153
Former US Navy & Palma Rifle Team Member
NRA High Power Master & Long Range High Master
NRA Smallbore Prone Master