After the frost hits and the asparagus and rhubarb tops turn brown, cut them back to the ground and prepare the soil as you would for spring planting. Water well and add mulch to the rhubarb so the roots do not heave out of the soil during winter. Since asparagus is planted deeper it does not require mulch. (Cynthia Domenghini)
Here are K-State resources for more detail on
asparagus: http://www.bookstore.ksre.ksu.edu/pubs/mf319.pdf
and rhubarb: http://www.bookstore.ksre.ksu.edu/pubs/ep99.pdf