I think it's totally dependant on climate. This tree did not like an August repot in VA but didn't mind March at all. More northern areas are different I'm sure. The one tree I've found that deals well with summer repots here is Crape Myrtle.
My opinion it is not especially the climate, it's what actions you take for aftercare.
I repotted in early summer, still thriving... but after care was
1) three weeks under 50% shade cloth
2) misting foliage 3 times/day
3) do not prune/decandle
To me, it makes sense to repot a mugo in early or midsummer, because that's when the roots are growing. So the fine hair roots that you lose during repotting are quickly replaced and so the mugo will recover more quickly. Not in spring, because all the energy goes into developing the buds to candles