Question about removing unwanted trees in winter

My lilac tree-forest have been spreading and there's a lot of it I want removed.
If I cut it down when there's frost in the ground, will it harm the 'mother' trees?

What about a dog rose bush?

 

Hi

Lilac do tend to send up new growth (suckers) all over the place cutting out now is the right time and no it wont effect the mother plant same with the dog rose.

You need to pull them of the main root rather than cut then as they will regrow (if you can)

 

Thanks a bunch! Is it possible to stop them from regrowing if I can't get to the roots? Like...drown them in chemicals or something...?

 

you could but you will kill or badly damage the main tree you want to keep, all on the same root system .

Just have to take your time and do a little bit each day would be best ........