I rarely gate things, but when I do I find it really useful to set triggers for particular frequencies. The gate plugin from Reaper (which you can download the VST separately like I have - you don't actually need to be using Reaper) allows you to set the gate to only trigger for sounds between particular frequencies. You can also set up sidechains with gates and use an EQ for the same effect.
This allows you to be more specific and precise with how the gate is triggered, for example you can have it so it listens only between 200 and 500hz, reducing the chance that highs from the hi-hats will cause a false trigger.
Other than that, try to reduce the amount of hi-hats in the snare mic to begin with. Use the polar pattern of the mic to your advantage and try to angle the null towards the hats. Its surprising how often people complain about hi-hat bleed yet they have the snare mic facing from the front of the kit towards the drummer; practically pointing at the hi-hats!
Instead, have the snare mic coming in from the side so its under the hi-hats. You'll need to check that the mic won't get hit when the drummer plays the hats and, if needed, persuade the drummer to raise the height of the hi-hats by a few inches. Try as hard as possible to have the rear of the mic pointing straight at the hats (this is all assuming you're using cardioid mics
)!
Alternatively you can try to live with the hats in the snare track (apart from if you're doing metal or other genres with stereotypically isolated and separated drum sounds). It may sound horrible solo'd by itself, but look at the kit as a whole - once its in the mix you probably wouldn't notice it anyway. After all you should be aiming for the best possible sound from the overheads and just use spot mics to reinforce parts of the kit. This may even go as far as cutting most of the highs in the snare track (which would solve the hi-hats problem anyway) and keeping it low in the mix, just to add a bit of extra low/mid-end punch to the snare sound in the overheads.
So I think I reached a bit of a different conclusion at the end there, which is to reduce the amount you listen to the track individually (ban yourself from using the solo button
!) and think about how they fit together as a whole.
EDIT: I saw you mentioned toms... quite often I find myself manually cutting up tom tracks and taking out the silence myself. It doesn't take long, especially on a song without many tom hits.