How does the Eglu stay warm if the door is open for the rabbit to come in and out?

All of the Eglus are twin-walled to trap air and insulate the coop, making it suitable for year-round use, even if the door is open. 

You can add extra bedding or straw into the hutch to keep them warm through winter. Extreme temperature jackets are available for all Eglus to keep your pets warm through the winter months.

You can find the Eglu Go blanket here: 

https://www.omlet.co.uk/shop/chicken_keeping/eglu_extreme_temperature_protection/23921/extreme_temperature_blanket_for_eglu_go_green/