There were only 607 true DC-3 airliners produced between 1935 and 1942 when production at all Douglas plants switched to C-47s and R4Ds. I don't believe that DC-3's had cargo doors, something you'd need to get a horse through the door of a DC-3
But in 1943 all the C-47s/Dakotas are going to the military.
Also please remember that in 1943 DC-3s were still NEW airplanes. I get the impression that you want a beat up old bird, flying the back woods of Canada, for the story which also doen't fit the time.
Bump the story up to 1954 and the plane would fit.