Each of my wirehairs encountered fences at speed. The wiser, Button, didn't suffer too much, but once cut the pad of a paw horrifically from a strand, or some old farm machinery in the ground. It was then I learned that dogs don't get tetanus and she didn't need a special shot. (As an aside, the Vet wanted to knock her out for the stitching. I told him Novocaine was fine and I'd hold her. He was skeptical, but went ahead. She was fine. He said he'd mostly had farm dogs around and he wouldn't take the chance of them being conscious when he stitched. )
The less-wise, Young Bert, the not-right dog, ripped his chest open twice. Each time was the late Saturday on a Monday holiday week-end. I clipped, then shaved the site, washed it with soapy, warm water, and finally spilled some hydrogen peroxide on the deep gashes. When I got a Vet, she said that since it was a few days past, and since the cuts healed from the inside-out anyway, she'd just as soon leave them alone.
She also said I should use alcohol instead of Hydrogen Peroxide.
Mick, the Springer, isn't as single-minded in his pursuits to date.
But, as a general rule, I'd follow Ken's advice.