Garden plants need nutrients for healthy growth, so hobby gardeners give them fertilizer. But, beginning in the fall, plants enter a dormant period.
If you keep fertilizing at this point, you could inadvertently damage your plants by activating growth with all those normally beneficial nutrients. This late growth, not being hardened for the winter, will most likely fall prey to the first frosts.
There are other reasons not to fertilize plants during their rest period, and they have to do with the environment. During the coldest months, plants barely take up nutrients. Fertilizers, unused, slowly seep into lower layers of soil and from there can end up in the groundwater.