As for dual purpose poles I only use two trekking poles hiking in. These are typically easier miles with more weight, perfect for poles. Once actively hunting I want at least one hand free (more often 2) whether scrambling on scree fields and large rock to get to glassing locations in the dark or doing beetle kill yoga. I have a lot less weight on these days: gun, kill kit, e-kit, a few calories and water. When hunting with a partner we hike in with 2 each and donate one each for the shelter.
As for styles of shelters any decent sil-nylon can work great in any weather. It’s all about site selection and set-up. Even if you are rocking an expedition grade mountaineering double wall shelter you have to guy it out for storms. Any tent in a storm must be guyed out if you want to ensure you don’t have a failure. IMO learning to properly guy out shelters is a really important skill to have in the back country regardless of what you are doing.
I currently run three trekking pole shelters:
Seek Outside Cimarron Light for fall through spring mountain hunting with 2-3 people. A
Big Agnes Scout for solo hunting or summer BC trips with my 6 yo and a Dyneema tarp 10x10 I pitch for solo hunts when going more minimal. All of these options use two trekking poles. The only time I prefer a floored shelter is when mosquitos are really bad. Otherwise floorless is way more convenient.