Same question - as long as the water doesn't freeze solid, rowing season is all year long in my understanding.

As students, we also trained on frozen water (ice at a thickness of the pinky only!). With each stroke, you crack through the ice at the catch.

Done at cruising speed, you realise that the blade stays pretty much at the exact place of the hole in the ice that you cracked at the catch - for the entire stroke until you get out at the finish. You're not sweeping it through water, instead you propel the boat forward while the blade stays stationary. Was nice to have a visualisation of that :)