First, know that Amaryllis bulbs do NOT naturally require a dormant period - i.e.. a forced rest over winter without light and water where the bulbs are stored at cool temperatures.

These plants do grow year 'round in their native habitats. Some may require a resting period in the dryer cooler "winters" during which time growth slows down, but that is not the same as dormancy.

Basically, continue to provide your Amaryllis with bright light over the winter months and continue to water it on a reduce watering schedule, allowing it to dry out just a bit in between waterings. Some plants may not produce any new leaves, while others may lose some of their lower leaves.

Forcing Dormancy
Reduce watering and let all leaves die back about 16 weeks before you wish to have blooms. Remove all leaves, and then place the bulb in a dark closet, storage room, or basement where temperatures remain about 55 degrees and the air is dry (you don't want the bulbs to rot). After about 8 weeks, you can water the bulb once and move it into warmer brighter conditions to break dormancy. Keep the bulb just moist until new growth appears. It will take another 8-10 weeks for the bulb to flower. This is not an exact science, so allow a week or two on either side for error.   See Stage 1 Amaryllis care for more information on bulb care. Forced dormancy can stress the plants so do not repeat this every year with the same plant

You can also wait until the bulbs naturally emerge from dormancy, rather than forcing them. This may be useful strategy if you do not have enough windowsills to 'house' your amaryllis plants over winter. Let the plants die back in late November, or whenever temperatures dip to about 55 degrees at night. Then store the bulb as described above, and wait for it to natually break dormancy, usually in the spring. Follow Stage 1 Amaryllis care.  

NOTE: There are some amaryllis species and hybrids that should NOT be allowed to go dormant, such as Amaryllis papilio and its hybrids.