Pteranodon the OP is also a family member, isn't she?
It may well be she doesn't want to go to work any more than he wants to go out and play. She is working to earn money for the family (unless she works for the joy of it and to buy handbags - I guess some people do).
Either way in every 24 hours there is room to accommodate the needs and wishes of both equally important humans - mother and child. Child wants to stay in and play, mother needs to do some errands and wants (sometimes boarderline needs, depending how the day is going) some fresh air.
1 hour outside is actually not telling the child his wishes are not important. 1 hour outside leaves 11 hours inside presumably - child has still had his way most of the day!
There is also the fact that a caring adult knows better than a 3 year old what he needs even though he knows what he wants. Sometimes I have to make my kids go outdoors for their own good even when I don't want to either! Most of the time they do want to, so I have not had the specific "want to stay indoors all the time, all winter" problem, but of course there are things 3 year olds don't want to do, which their parents would rather not bother with either, but enforce for the child's sake (take antibiotics, eat vegetables, go to bed at a time that will allow the child sufficient sleep, not eat an entire 100g bar of chocolate at once...)
You can respect a child's wants but know that they are not compatible with the child's needs, and you can decide to put your foot down about how one hour out of 12-14 waking hours are spent, without failing to be kind, to empathise, or to respect the child.
Allowing a child to stay indoors 24 hours a day for 4 days a week (with the other 3 days also probably spent mainly indoors at childcare) is not better for the child than allowing them to choose how to spend 11-13 hours a day with the caveat that they spend one hour outdoors.
You can't make a child play but you can take them for a walk, to feed the ducks, to swing on a swing, go for a bike/ balance bike/ scooter ride in the park, or if they out and out won't walk or cycle or play stick them in a push chair wrapped up snug and at least get both of you some air!
An hour outdoors improves the mood of both adults and children generally... On the very occasional days we are all stuck indoors all day everybody gets grumpy IME.