It's funny I was just talking about this with someone. And my observation is that Ohio state doesn't really have a distinctive "style" system or mentality. More that their coaches are good at developing/maximizing a particular wrestlers individual style and skills then peaking them.
I can't speak to Snyder or Martin because I haven't seen footage of them in high school. But almost all of the Ohio state wrestlers I've seen footage of in high school. The Stiebers, Jaggers, Bergman, Pucillo, Tomasello etc. all look like they got better at what they did in high school, not like they started being indoctrinated in a system like you see in at least some Iowa and OSU guys.
The one exception I can for sure say is the Jordan Brothers, they are much more wide open and diverse in offense now. In high school they were square stance, methodical movement, hands low, crisp technical sweeps