Can I trim my chrysanthemums and winter them I seed trays I my

Once they have finished flowering yes you can. The pieces you lift are called stools.

This is what the RHS says
Once flowering has finished, cut down the stems to about 20cm (8in) tall, to produce what is known as a stool

Lift the shortened plants and shake off the soil from the roots

Snip off any green shoots and leaves, so you have bare stems

Label each plant, if you have several different types

Stand the stools in a shallow tray, on a 5cm (2in) layer of slightly damp compost. Cover the roots lightly with loose compost.

Store in a cold but frost-free location, such as a cool greenhouse or conservatory, or a garage

Keep the compost just moist through the winter

https://www.rhs.org.uk/plants/chrysanthemum/growing-guide

Thank you