You'd be running into significant problems long before headwind killed operations due to zero flow rate.
As has been said crosswinds much above 35-45 knots are going to be above most aircraft's crosswind limits. Even with the wind blowing along the runway some aircraft have a maximum wind speed for ground operation (50-70 knots), and then again many aircraft have a maximum wind speed for door opening/closing ( again typically up around 50 -70 knots).
I'm sure there will limits for the ground folk as well - rumour has it the new tower at LHR has a wind limit, above which it cannot be occupied - any truth in that?