Yes however there are different ways to go about this, it depends on what you need the setup for.
Method 1: Purchase another Freeview Box / TV for the other room.
This is a straight forward way of allowing Freeview in the other room, in newer homes you will be able to connect a new set top box or Freeview Built-in Television into a wall socket, depending on the area and what services are available will determine if you can watch Freeview via UHF or via Satellite. If you are in an older house, you may need to do a few more things to allow another Freeview signal into your other room - most people purchase a Two or Three Way Splitter which splits the signals from the Satellite Dish into your main room (Lounge) and another into the bedroom/s.
Method 2: Purchase a SmartVU Freeview Streaming Box
Freeview along with DISH TV offers a small device which allows you to convert any HD TV into a Smart TV, but with the addition of Streaming selected Freeview Channels via the internet. You will need a solid internet connection with a plan that can handle streaming (Like an Unlimited Plan) You won;t need to connect the device to the Satellite Dish or UHF aerial, all it needs is power (Which you can supply from the TV's USB port or via the supplied AC Wall Adapter. you can find out more about this device here
There are also other methods people use as well, share us how you set up more rooms with Freeview below, and if you have any questions .