Snugbug was the name on the children's sleeping bags when my two were little. Proper mummy shaped bags in iirc three different sizes and a range of colours. Wouldn't do for Winter without warmth above and below but did fine for Spring through to Autumn.
Honestly, best advice for a kiddie is to buy a single bed quilt with a cotton cover. Run it through a dye if you want, and then cut it to shape and just whip stitch all the raw edges together. You could cover those with bias binding if you choose to make a really tidy job of it. Under £20 for one that'd be at least as warm as a 3-4 season bag.
If you make a draw cord at hood, just use the lock from an old anorak, or elasticate it. You can add a zip or velcro if you like, even a baffle.
I've done a couple, you don't even need a sewing machine, just a decent needle and either strong or doubled thread.
It'll do a year or so no bother at all, and children have this disconcerting habit of growing
so just make another as needed and pass the first one along
If you really need to oomph up the warmth, then I'd make a liner from one of those sheepskin type fleece undersheet things and stitch that in too. (make sure its tacked/stitched at the side seams and the foot too, to stop it fankling around the youngster in the night) Though fleece throws are pretty cheap these days. Kind of sweaty though if the child runs hot.
We had some bitter cold Winters when I was very little. My mum cut down a down sleeping bag for me. It was warm, but I hated that thing. Never much of a fan of feathers, I can ay feel the wee quills.
Bedsocks aren't such a daft idea
and neither is a hot water bottle in the bag a little while before the child coories down.
If you keep the child close to you and throw a blanket over the top of both bags, it'll be even warmer too.
Used to sleep like that when down at the boat at this time of year when we were little. Perishing cold in the canvas tent when the tilley light was turned off for the night.
M