Many climbers use trekking poles, but restrict their use to the approach trail or low angle snow. When the terrain gets steeper, most people put both poles in the pack and use only their ice axe. On moderate snow ascents, try using one pole in combination with your ice axe. Keep your axe in your uphill hand, and the extended pole on the downhill side. This is especially nice on traverses.
This technique has two benefits: One, you create a lot of additional stability with the downhill pole, adding greatly to balance and confidence. Second, once you get into the rhythm, you can lean a bit on the downhill pole and use some arm muscle to push uphill, taking some weight off your legs. Take some load off your legs, feel a lot more in balance, and climb faster - what’s not to like?
Here’s a photo of a climber traversing a moderate snow of about 35 degrees on the lower approach to the Cathedral Ridge route on the northwest side of Mt. Hood. Note the pole in the downhill hand, axe on lanyard in her uphill hand. She walks quickly, in balance, and the pole is there to keep her that way.
If you need any more evidence, here’s a photo of Ed Viesturs on the summit of Nanga Parbat, showing him with an axe in one hand and . . . you guessed it, a trekking pole in the other.