Lower pressures provide more traction is low grip conditions on snow and ice.
We use 12 to 22 psi while racing on ice with ice racers using winter tires (no studs) but we use inner tubes to prevent them from loosing air when the sidewalls flex or we hit a bump while sliding sideways. (don't worry I don't use my Insight for ice racing because the cars get bumped often)
I would suggest using the Honda recommended pressures of 38/35 psi most of the winter and when it's slippery with snow and ice maybe lowering the tire pressures down to about 32 psi temporarily. But when it's not slippery anymore pump then them to 38/35 to improve dry grip performance and fuel economy.
Even the cheapest winter tires are better on ice and snow then the most expensive all season tires