Is the discharge clear and watery or white/creamy coloured?
He is a white bun looks a creamy colour on his fur
That is indicative of infection so I would get your Vet to check him over
I wouldn't bring him in unless he shows signs of being very poorly..as the change from indoor to outdoors can make them worse..and also you will then have trouble putting him back outside in the winter
Fingers crossed it clears up soon x
I would definitely keep him indoor. When a rabbit is sick, he cannot fight the cold and fight the sickness at the same time. In fact, he should stay in a room that is warmer than average room temp. to boost his immune system