Yes, as has been described, ATC will pass to the airport the predicted impact of forecast weather in terms of capacity. It will also pass on the predicted impact in terms of delays due to the reduction in capacity.
The airport can decide to request that airlines reduce their schedules by cancelling, or, and this is the case for LHR, it can decide to invoke a process which all the airlines have signed up to which forces them to cancel a proportion of flights.
See here:
https://www.acl-uk.org/wp-content/up...localrule4.pdf