I hang under cover from 4pm to 8pm, so the actual drips come off, then they come in the house, over the dining chairs!
Because they are never on in the stable, they don't smell particularly. If a liner is horse-grease smell, it can go in the wash, 30 quick wash. If they come in muddy, I hose off whilst still on the horse then follow the above.
Mine are Rambo and Rhino, always dry by 5am, and the heating isn't on overnight (although the house has residual warmth).
Premier Equine rugs, or any that are not truly waterproof, take ages to dry. I did try cheaper rugs than Rambo, but they only stayed waterproof for a season. I have not find re-proofing rugs to make them truly waterproof. Any rugs that are not truly waterproof are moved on pronto, before I can be tempted to use them, latest was a Premier Equine one that came with Rigsby that was too heavy. People pay money for non waterproof outdoor rugs, mainly for stable use I guess? But I prefer stable rugs for indoors.
I NEVER wash outdoor rugs, other than a hose off and washing the separate liners. It takes away the waterproofness.
Before anyone thinks my approach is £££££££££, my Rambos seem to last years and years, and I think end up cheaper than cheaper ones that need replacing. I had an original green one for about 18 years, still waterproof but I downsized horse and it was too big
