Ive been riding for 20 plus years. When I get stuck on flats I either push with my back leg, un-strap and walk, or have my skier wife tow me - and thats in order from first to last resort. Never have I seen anyone on a snowboard bring a pole along.
I have yet to see another Tuber with a kayak paddle...
That said one of my best friends was Jake Burton's first team rider. Before Burton put steel edges on the board. Got fired from his Ski School Director position in Vermont ‘cause he never ride ski's anymore.