When I made my original plan for this project, I not only looked at the snow groomer. I did choose it as target because it required the most complex solution (because of the 12V power it needed). But since there are much more toys in my kids room, and I intended from the beginning to convert more than one over to be powered by rechargeable batteries (and wireless charging). Thats why I ordered a cheap Qi receiver off Ebay and measured its performance too.
So while I was busy to rectify all the bugs I introduced, I thought it might be a good time to do something simple that will probably work right from the beginning. So I borrowed another car from my son and started working.
It turned out that inside these RC cars there is usually not so much space left. So I was not able to fit a larger LiIon battery in. Thats why I settled with a 650mAh one (its actually a phone battery). For charging I built a small circuit using the LTC4054, since it needs just two external components. I already used it for my wireless charged night light, so I had some experiences with it. I built the charger on a small SOT32 breakout board, and isolated it with heat shrink tube (the green part in the picture above).
To connect the Qi receiver I drilled small hole in the battery compartment. Originally I thought I might put the whole circuit there, but its to small to fit a LiIon battery (I would need to look for a square one):
I wired up everything so I can easily remove the additional circuit
So the receiver just fits on top of the partitions, but I need to fold it. Then it fits perfectly into the space reserved for three AA cells:
After wiring everything together, its time put the car on the base station. And there it sits, charging its battery proudly:
I used clear acrylic for the enclosure, since its easy to handle, and I can re-use the internal LEDs for monitoring. I just added a current sense circuit with an attached comparator to drive a red LED (the one in the front). It turns on then the base station draws more than 500 mA, which is about the current drawn during charging. That way I get both a signal when the toy is positioned correctly 8the LED turns on) and when charging has ended (it turns off again).
So that took about half of yesterdays evening, and lightened up my mood again 
And my son hopefully will be happy that he now doesn't need to wait for me to replace the batteries in the car anymore. Win-Win!