Yes, that happens to me, too.
I've only been outside walking 3 times now, but it happens each time.
I thought it was all the trees, grass and outdoor things blooming.
I have a lot of allergies to stuff like oak trees, grass, molds, ragweed, cottonwoods, etc.

It could also be that our throats get dried out more from all the extra breathing involved. Maybe the dryness irritates the throat and brings on a coughin spell.

I'm going to try bringing a bottle of water with me next time and see if that makes a difference.
You might try this as well.