What type of carpet suggestions for a log cabin

What is your flooring now? Do you want wall to wall carpet or some really good quality, well placed rugs?

Are there any drafts coming from the floor?

an actual cabin? floor cloths, or any sort of 'rag' rug (penny rugs, crocheted or braided rugs, 'needle-punch' rugs, or 'persian' rugs with simple or geometric designs) will look best with the rustic walls.

if you want to mimic the look 'of' a cabin without it actually being rustic, and want carpet? I would go with the best quality tufted (not berber or 'loop') rug in a medium-dark neutral in brown, grey, or softer greens (I've seen 'moss' colored carpets used to good effect)

We have a cabin too, so here are my suggestions: something dark or multi-colored to hide dirt, because it's not vacuumed as often as a full time house; durable obviously, maybe even carpet tiles so you can swap out stained ones instead of cleaning every time. Oh, and soft on your feet if you tend to walk around barefoot!

Indoor-outdoor carpet would be best.

Something with a texture/nubby like berber.