You want to propagate in spring/summer for the best chance at a successful propagation. Make sure that any wintery cold weather is behind you so that your new plants are growing in warmer brighter months as this will speed up growth and help them recover from any post-propagation stress!
As you will be dividing the plant, rather than growing cuttings it won’t matter so much about doing it at the start of the warm weather as the process is much quicker. Propagating  Asparagus Ferns in autumn or winter is still possible but will mean your new, now less mature plants won’t be growing as fast and the risk of root rot is much higher!