My family did that. We've had french bulldogs for 10 years, and when my parents' lost theirs, they got a basenji. French bulldogs and pugs are very similar in more than just looks, as I'm sure you know! There are a lot of differences between those breeds and the basenji, but also a lot of similarities. At least that's my experience, but that's only with one basenji that's a little over 1 year old.
The cold is not really a problem for Yuna. Rain, on the other hand...that she hates. But cold and snow is pretty much like with all short haired breeds. Put a coat on her, maybe boots/socks, and don't stay still for long. Kinda like with people.
If I were to name the two biggest differences, it's that my french bulldogs have always been over social with strangers, annoyingly so at times. Yuna is just polite but reserved. The other thing is the range off leash + the hunting instinct. French bulldogs and pugs usually don't have much of that, but it's something you have to expect to find in a basenji.
Oh, I said two, but I have a third difference that is...tricky sometimes. Yuna is not much taller than a french bulldog, and she weighs less, but her reach is insane in comparison. Not to mention that she's more agile. Meaning that if you have a thieving puppy or young dog (I'm looking at you, Yuna!) it will have easy access to everything. So Yuna and her "big sister" are about the same size, but Yuna has twice the reach... The bonus is that if you're the sloppy type that leaves things out on the table or kitchen counter, you will soon learn not to do that.