You could opt not to feed the reindeer but a better idea is to put something else out instead that will actually help the environment. I am a little late perhaps but maybe not, as a lot of plants are still flowering or have gone over leaving seeds. Collect these up (or buy seeds) and have a little fun with them.
Inside go the seeds and these can be sprinkled on the ground wherever you want. The bed will first need to be raked and weeded and these do need to be the type of seeds that you can sow directly into the ground at this time of year, not the type you have to sow into seed trays first. This is what it says on the back:
here for butterflies and here for more general pollinators including bees. You can also buy seed mixes and seeds especially aimed at pollinators from many seed merchants.
Do reindeer eat seeds? Well, they certainly don't eat sweets!