If you organise machinery to come and do work on your land in the middle of winter, the result is inevitable.
I think you would get short shrift if you attempt to complain.
If you don't want to rut / chew up your land, organise work to be done at a dry time. eg spring , summer , autumn or as conditions dictate.
As others have said, grass is very resilient, when things dry up a bit, give it a good harrowing, chuck a bit of grass seed on if, harrow again once , roll and it will be good as new before you know it.