FWIW - I never even need to adjust my brake controller. Since it's accelerometer based, it's already putting out less power than stopping on pavement. I've had a couple steep intersection where I had to apply the trailer brakes manually, because the controller didn't sense send enough power. Granted, my trailer brakes are marginal...
The only time I got this trailer sideways, I wasn't braking, but I did come through a snowy roundabout a wee too fast.
And a few of you may remember about 12 years ago when I broke the front off my weekend warrior. That all started when my trailer brakes faulted coming into a downhill curve in freezing rain. So.... I definitely using trailer brakes!