You don't say how old he is, but I have a 3 year old, and we tend to try and get somewhere in the morning and then play at home in the afternoon. We visit woods, playgrounds, the canal, a local field, beach/dunes, skate park. If we have nothing else to do then a trip round the estate on his trike and a stop at the local shop gives him some exercise. We have a bike, scooter and trike to make use of and some outdoor toys like a net, bucket and spare, kite and litter picker. We have a garden too so can play ball or badminton or in the mud kitchen. I have a couple of mum friends with similar ages children so we take exercise together with the kids on bikes once or twice a week.
In the afternoons we have lunch and half an hour of tele, then he can play or we paint or bake/cook or he helps me with the hoovering or laundry. He will play on his own for ages with play doh or kinetic sand, otherwise we read, play hide and seek, make things for special occasions like cards, decorations, or just let him play in the sink and pretend to wash up. I let him have a bit of bored time too so he finds something on his own to do, so I can tidy the place up or cook dinner. We also have a few games and jig saws to play together and a music box for "jamming" sessions.
He loves to help me and also learn to do things for himself so he has learnt to pour water from his own little jug and he has some kids knives so he can chop his own fruit. He can help make toast, tea, coffee, measure. Even getting dressed is a learning opportunity, you can teach him to get his coat or hoodie on easily by lying flat on the floor and letting him put his arms in and flip. Wellies are easy to put on, then pants and trousers.
It is really hard to keep them going all day in this weather, it does get better when the weather improves and you can play outside for longer periods. The older they get the more independent play you can encourage too. Spring is on its way! Have hope!