So you used something like cotton batting (can't be wool roving if it's cotton) to make thrums in acrylic mittens? I would guess the acrylic is machine wash and dryable, but I'd be worried about the cotton thrums, so I would stick to the hand (or at least cold) wash, drip dry.
Have you worn them yet? With cotton thrums, I'd also be worried that sweaty hands would stay wet (I had a pair of thrummed mits long ago for skiing, and my hands would sweat, but the wool was keeping them mostly dry, not soggy).
Hope they work out for you!