The temperature will have an effect on your smoking, but not nearly as much as wind. Wind seems to suck the heat right out of a smoker. If it's windy, rig up some kind of windbreak.
I'm assuming your home made smoker isn't insulated, so that will make it tougher to keep your smoking temps up where you want them. Some of the folks around here wrap moving pads or welding blankets around their smokers to help hold in the heat.
If you're having problems keeping the temps up in your smoker, there's nothing wrong with opting for the oven to finish the job. That's better than having the meat stay in the danger zone for too long and then having people get sick.
Just my $.02. Hope it's helpful.