I don't use any poles.I suppose as a kid in upper NY roaming gorges in summer and snowy hills in winter I learned to get around with things I would just tend to lose/leave behind. Then I was made to watch workers' comp avoidance "MoveSMART" videos about 12 years ago (recall mentioning this in another thread) which showed tips about moving on slippery surfaces and which were credited by my then-Fortune 500 employer with dramatic claim reduction moving on slippery floors, steps, etc. in its production facilities. The last video they made me watch was one that was done for the USFS.
Some tips I remember after all these years are:
Watch where your belly button goes (close enough to center of gravity for most folks). Belly button over feet is good. Belly button in front of feet is not good due to slipping causing knee and face plants. In the video's opinion poles are not good because slip or misplant inevitably causes belly button in front of feet meaning the fall is more injurious to knees or face.
Keep Your Crown - Look down with eyes not head, pretend you're wearing a crown on your head that you can't drop. Head weighs enough that looking with head not with eyes moves center of gravity in front of belly button thence in front of feet leading to front plant.
On a slippery surface, keep one foot planted flat under your belly button and move the front foot forward until the other foot's planted then shift weight to it. Imagine an invisible line pulling you forward, tied to your belly button.
Don't flail arms or put arms out for balance, that moves center of gravity away from your belly button to where you can't control it. Plus you then fall on your hand or wrist for expensive injuries.
Following these rules, if you fall you land on your butt then can get right back up again. I've got much experience with this too.