No. The current requirement to switch from analog to digital only applies to full-power broadcast TV stations, which use public airwaves to provide free over-the-air programming.
However, as cable providers convert to digital transmissions over their systems, you may need to subscribe to their digital tier to continue to receive non-broadcast programming.
Can my cable system move programming to a digital tier that makes me subscribe to digital service?
Your cable system decides when and whether to carry programming on a digital tier, which may mean that you will need digital equipment. However, all of your local stations will continue to be available in analog format for as long as your cable system offers any analog service.