What kind of knitting style is this?

To me, this looks like garter stitch done with bulky yarn on big needles. Knit every row. (or if you're weird like me, purl every row...I prefer the purl stitch) Really simple. Just one stitch to learn! It looks like the artist knit a long scarf then stitched the ends together to turn it into a cowl.

If you want to replicate it, here's what I would suggest:

Using super bulky or bulky weight yarn (sorry, don't know how much you'll need, probably at least 300 yards) and a pair of size 11 or 13 needles, cast on 15 to 20 stitches.

Knit every row even until piece measures 7 feet in length, bind off loosely.

Sew ends together, taking care not to twist if you want a cowl, or twisting once if you want a mobius scarf.

This is just garter stitch, the easiest one to learn. Just knit every stitch of every row.

Try www.knittinghelp.com if you haven't learned the basics yet.