Could you look at the manufacturer's instructions?, There is possibly guidance on tyres there.

Wouldnt this be a PUWER item

Are the tyres

- suitable for use, and for the purpose and conditions in which it is used;
- maintained in a safe condition for use so that people’s health and safety is not at risk; and

Does a tread make a difference in muddy conditions?

Evening,
As other posters have suggested, check the contract, I would also check (if you can) what your contractor's tender document said in relationship to maintenance and standard of equipment. They may have been required to provide a H&S Policy (not just the statement) which if they have large plant should contain reference to maintenance and possibly tyre wear.
Other sources you may wish to try are their Risk Assessments (is a control measure to replace tyres after x number of hours? or regular checks to be carried out on tyres? if the latter then who signs that they are safe). Safe Systems of Work/Method Statements/Safe Codes of Practice may also provide you with guidance to what they are supposed to be doing.

In my last company I had a problem with bald tyres on heavy duty fork lifts, tugmaster units and trailers, I wrote a memo to the General & Engineering Managers saying that in my opinion the company was not complying to PUWER but more pertinently the Dock regulations (appropriate parts of both forming part of the appendix). I then followed this memo up with weekly checks on the vehicles and a status report. This led to very heated exchanges in safety meetings and management meetings but in the end the executive made money available to change tyres regularly.

So I would make my concerns known to my line manager and the contractor in writing asking the latter for their written assurance that these tyres were safe in all conditions they were likely to encounter but before I wrote my memo I would also contact the tyre manufacturer, possibly send some photos showing the conditions remembering the tyre manufacturer has a vested interest in selling more tyres.
I would have a quiet word with some of the vehicle drivers asking if they had had any problems e.g. braking, sliding.

Remember I do not know your circumstances and can only say what I think I would do from my own experience. Also remember once you have pointed out your concerns you have to then keep chasing up as if something does happen you will be required to demonstrate that you continued to express your fears but were ignored.

Hope some of this proves useful.

Take Care