All you need is a low-voltage control timer if you're not going to install an aquastat on the thing. A setback thermostat could be used for this, but you need two wires - 24vac from the low-voltage transformer, which when the timer kicks on and the temp is not met would then connect that 24vac to the control line of the mixing valve (the other side of that transformer would already be connected to that device to then complete the circuit - the thermostat is just a single pole, normally open switch, well, single pole, double throw if it also works with cooling). Typically, that would be a zone valve, not a mixing valve, which would often be upstream of it.
You may not get all that much warmth to the towels. Typical radiant floor heating loops often are pretty low temperature - tends to work better with radiators where you're running hotter water. I have an electric heated towel bar connected to an in-wall timer (line voltage) that has built-in heat limiter thermostats that cycle, once it reaches its set temp. Even though I do have radiant heated floor there, this allows me to have a warm towel throughout the year, rather than only during the heating season (it seemed like a poor use of energy to bring the boiler up to temp to just heat the towel bar with its VERY small load). There's enough air movement around it that, even though the bars are too hot to touch for long, only get the towels warm, and if they are really thick, the outer surface may not get warm. Still, it's nice on a cold winter day and it does dry them much quicker than just hanging them up.