buy good snow gear and coats for the dogs. 
I'm no Basenji expert since I've only had one. And, I don't want to start a dog park argument. I'll just share my experience.
Jengo LOVED running free, but he's a Basenji. Can't do that cause... cars. The dog park near our house is HUGE. A big completely enclosed lawn area the size of a football field with towering oak trees. We were OCD about keeping Jengo's vaccinations up to date. He was chipped and wore a collar with contact and rabies tags 24/7. He loved the dog park, but not all the dogs there. He hated any dog of any size that would try to dominate him in any way. He rarely instigated it, but he never tolerated it meaning regardless of size... he wouldn't back down. He also hated if another dog approached him from behind and would snap immediately.
My solution was to stay near him and to keep moving. We would walk laps around the perimeter and by about the second or third lap he'd been or had checked out all the other dogs. Then things were good. If I saw that he was getting anxious I'd usually catch it before he reacted and would tell him "Easy". 9 times out 10 that was enough. I'd also make sure that he was aware of dogs in our vicinity so that he wouldn't be surprised if they came from behind. We went to the park for years. He never caught anything that I was aware of. I did pick him up and leave if there was another dog he and/or I weren't comfortable with. And, I also recall walking away before ever entering the park if there was a dog we didn't like already there.
I guess my point is that part of protecting your dog and others is knowing and focusing on them without over-reacting at the same time. I don't want to set him off. But, I want to know what he's going to do before he does. You have to read him. All dogs give signals one way or another. Tune in to your dog, not the other people at the park. I liked the other people at the park, but I wasn't there for them. My focus was always on Jengo.
