Very hard. If a race is cancelled, everybody goes home (instead of buying tickets, beer, hotdogs etc) and they show X-Games from 2 years ago on TV instead (good bye commercial revenue). They have nothing to gain from not racing in the rain. The physics are too much to overcome.
At 550kg (1200 lbs) a F1 car is less than half the weight of a Mini.
The amount of aerodynamic downforce produced by the front and rear wings and the car underbody is amazing. Once the car is travelling over 160 kph, an F1 car can generate enough downforce to equal it’s own weight.
NASCAR has, in the past, brought the rain tires out in practice at Watkins Glen and at one of the Suzuka exhibitions. For them to be used, though, the cars have to have been equipped to accept a windshield wiper and have a brake light in the back window.
Interesting note: NASCAR has ordered all the teams to equip their cars for rain racing before the Mexico City Busch race in 3 weeks. Goodyear will be mounting all the hand-grooved rain tires in the event it rains.