40 amps is certainly no trickle charge but should not do any damage for such a short duration. My boat has a 100 A alternator on the yanmar 35 hp but it has a smart external multistage regulator.
I also have a charger on the farm with a 200 A position but not to be used for more than 5 seconds. Always charge at the lowest amperage you can to get a complete charge. Our fast charge is 30 A and I installed a timer in that outlet so cannot go over 2 hours.
Everything in that battery circuit has big cabling, right? 40 A should not be too much from a wire size perspective, nor a big battery for just 15 minutes. Unclear on tractor but think you meant 5105, which should have a good sized battery. If it was really cold, maybe charger or battery might make a little heat, and maybe some vapor/steam from battery - but smoke? I dunno. Newer smart chargers are good at sensing battery condition and won't throw amperage at it regardless of condition. Nonetheless good to have a manual charger to put on when you willfully want to override an auto charger, but good to babysit it like you did.
Bad connections are always a place to start. Having a boat has made me better at making good connections, sizing wire properly, use heat shrink tubing, etc. the salt air is tough on wiring, and hard run tractors can be too. Check charger connections too
Good luck, and sorry to hear about the snow. Since no more benefit from our freezes here, I'm over the winter thing. Insects were bad here last year, but these 25 degree nights aren't going to help that much anymore so bring on the sun. It was 70 and sunny here all weekend and the grass grew inches.