The idea of trainer specific tires is a recent concept, which IMO is simply a way to get folks to spend more.
We rode rollers and trainers for decades with standard smooth tread road tires. If we had a dedicated tire for the job it was to save dough by using the cheapest tire possible to avoid shredding our best tires.
So, unless it's to remove a good tire and ride a cheaper tire, feel free to use what's on your wheels now.
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