Is going in at Mudro and up the horse river a good way to get to Robinson Lake? My concern is where do you find a close by Canadian Border office to get permits checked?

I haven't been to Robinson in 10 years but you used to have to go through the Canadian Ranger Station on Lac la Croix from the west or at Prairie Portage from the east.

Years ago, you could go through Customs at PP, but now an RABC permit is required. You are allowed to use the portages on either side of the border lakes but Robinson is nowhere near the international border.

Day trip?
Overnight requires a reservation and then checking in at a Quetico Ranger Station...

Permit required even if you are not staying overnight. Our permit was checked by Canadian Ranger 10 days ago less than a half mile north of the border on Crooked Lake. They will NOT be sympathetic with "Oh, we must have lost our way!".

Have to go through the ranger station at PP or LaCroix. Robinson is a lake the rangers will check, as well as the bays on Crooked north of the border.

Best option is a Basswood River permit out of PP followed by the long paddle across Basswood. Theoretically you could take a tow to and from Moose, check in with the ranger and then drive to Mudro. Not sure how they would feel about that.

And you'll be traveling down the Horse to Basswood, not up. Current matters.