I have a few red Toads and a Toad is just hanging out in town. I see an option to buy a red Toad house, ostensibly for him. Are there any added benefits of purchasing this or are the colored Toad houses just cosmetic?
The red Toad houses are only purely cosmetic. I've checked, and they don't seem to do anything except give you a small bit of coins every now and then. Sorry about that!
From playing the game myself, I've found that the Toad Houses do have a function. Every now and then, the Toads will randomly appear holding a coin outside their house. Tapping on this this will grant you one coin, this is true to the red house but I do not know about how many coins you get from the other coloured houses. It's not much of a bonus, but it can still help.
Unfortunately I couldn't find a source for this information, there doesn't appear to be any form of wiki or guide for the game. So I'd assume that the more difficult to get houses, such as the ones that are only available after purchasing the game, will grant more coins than the easy to get red house. But I cannot confirm this as I haven't bought the game, and cannot find any information online that is relevant to the matter.
So other than this small bonus, the houses are purely cosmetic.
I recently collected some more coins from a red house, and I collected 4 coins instead of the 1 that I had experienced previously. This suggests that the amount of coins that you will receive is random; or possibly that the further along you are in the game, the more coins you'll collect.
They give you a small number of coins periodically.