Have your husband work on recall training.
Clickers work great.
Have hubby click the clicker and treat the dog in the house, for no reason.
Do that for one day.
Next day, put dog in backyard, have a clicker and click with treats in hand, I think you will be surprised how quickly these dogs learn the sound means good things.
We use beef jerky, but small pieces of cheese, or nuked hot dogs, cut in small pieces work well.
Just make sure the treat is WONDERFUL and this b will come whenever he gets the clicker cue…
That not the way that clicker training is traditionally used, though. If the dog has ever had any clicker training, or will in the future, this could confuse him. The clicker is intended to be the marker for desired behavior…not the cue. So it should look like this: teach the dog that click means here comes food -- click/treat click/treat. Then give the dog a cue in this case, calling him inside, and then click/treat when he complies.
If you teach the dog the click means 'that is correct, here comes your reward' and then you click when the dog is out at the back fence, he comes running, and you give him a treat, you are teaching him to hang out at the back fence.
If the OP wants the dog to come in when called by anybody..the very easiest way to train that is to shake a bag of treats at the back door (cue) and give him a treat every single time he comes thru the door for two weeks (or so)...then you could start to alternate rewards once the dog understand the command. You could also pair the orginial cue (bag of treats) with a word (we use "inside") so you didn't have to shake a bag each time.
Now, it if the OP doesn't care if the dog comes in when requested but wonders if it is okay for the dog to stay out? I haven't met a basenji yet that didn't know when he was too cold...or doesn't know how to come inside when given the opportunity if desired. So I would just suggest that the DH offers the dog the opportunity to come in fairly often when it starts to get cold.