I'd put a rug on the floor, shelves in the closet and a table and chair. How hot does your radiator get? And how fragile is it? If it's sturdy and never gets too hot, then all's good. If the radiator is fragile, put a long table in front of it.

Add an area rug, for some warmth and floor play. Child’s table and chair set for puzzles, coloring and crafts

I didn't point out the chalkboard wainscot on the closet photo, but that is a plus!

make it all playroom.

It will only be a playroom for a few years, make it special.

Actually, it doesn't seem like a good idea because there are too much corners, jambs and doorways - may be very traumatic..

That door looks like it goes to the outside, yes? I'm assuming this is a door that isn't used often or at all? If there's no danger of opening the door into your kid's play area and possibly hurting someone, then sure. Set it up as a play space. I'd leave the closet door off and fill the closet with shelving for toy and art supply storage that can easily be accessed by your kid. Get some carpet tiles in there to warm up the space and make it cheerful. Find a small table and chairs to put on the side opposite the closet for projects, puzzles, etc.

I would make sure the door is not able to be opened for sure but also sure you would have thought about that. I agree that some storage for sure and a good time to teach a child about clening up at the end of the day and nice to have a designated spot for all the kid clutter.I woudl not do any permanaent stuff on the walls but chalk boards hung like art anre awesome. A chair is a great idea and a little table and a chair for her if there is room. I agree the floor is probably pretty cold so a nice washable rug could be great. For me the big issue would be the kid clutter seen from the LR so the clean up at the end of day IMO is a must.

I’d put a fun hangingWhat a fun project! Please post photos when you are done. chair in the corner with the radiators, a little side table and sturdy lamp next to it, and then book storage around it on the walls. IKEA picture shelves or spice shelves would work well. The closet would have a desk with good lighting for art projects and include shelves for toy storage. You could use the empty wall next to the closet area for a blackboard, and bulletin board, just like Decoenthusiaste‘s picture. Great place to hang that art, and clutter is out of sight. Finish off with an area rug with a fluffy pile as high as possible to maintain clearance for the door and place a throw on the chair. 😊

Shoot! Couldn’t figure out how to edit to clean up my comment. I’d find a child size hanging chair for the corner by the door.😁

I'd start with a camera. There's space in there that you can't comfortably see from the other room.

Measure the space and find out if a carpet can be custom made and bound.

Keep a table pushed against the radiator so

Or get a radiator cover.

I would start by just putting his things there…see if he gravitates there…it feels confining to me…more like a space to just keep his things…to be put back after playtime…( a little lesson in responsibility by itself)…

I wouldn't dedicate an entry as a playspace. Is that an entry door? That is not a good idea it will be too tempying for your child to mess with. Add a pretty storage chest/cabinet and shelves in the closet but the play area should be elsewhere, somewhere you catn see what your child is doing.

I like btydrvn’s comment to start out as a place to store toys. I also like Shelley Miell’s idea of a hanging chair, and Lyn Nielsen’s suggestion to make it special. One way to do that is to wrap the space in a removable wallpaper.