I've used BT, a non-toxic substance derived from a naturally occurring, soil dwelling bacterium, Bacillus thuringiensis, for several years. I highly recommend it.

Not only is BT non-toxic to people, and to birds and other wildlife, it has to be ingested to kill, and will only kill caterpillars, because of the way it works on their digestive systems. It won't kill even harm butterfly caterpillars, since they don't eat leaves of trees you'd be spraying for winter moths.

The timing needs to be done carefully, since you want to get the cats after they've hatched and before they get too large. Try to pick a cloudy day, since sun breaks down BT. It takes a few days to kill, but apparently the leaf-eating stops almost immediately after they've eaten the stuff.

I wouldn't try treating a big tree completely (though you can get the lower branches, where the damage would be most visible), but I've used a pressurized sprayer from the hardware store and been able to adequately treat everything I thought needed help.

Dormant oil can be used, too, to smother the eggs, but I think that would have needed to be done earlier in the year - I haven't tried it myself.

There are lots of sources of info on line about this, I picked one that looked decent, although it's across the continent, to get you started.

Here is a link that might be useful: winter moth factsheet, washington state u

Thanks!