A tuned Delta will do the trick for the beginner gravel and snow events. Just be careful, brake early and put down power through the corner without touching the walls. Turn BEFORE the corner! Don't wait untill you're halfway through before turning in. Gravel and snow are NOT tarmac, don't treat them like it.
I had to do the tarmac event with a 'proper' car though. I used an untuned FT-86 (you win it in a beginner event) to great effect there, much easier to handle than any 4WD car.
Not sure what i used for gravel and snow for intermediate, but i used an R34 i got earlier to beat the tarmac event quite easily (only car i had that was near the 345 hp limit at the time). I did the advanced ones with a Citroen C4 i won later, quite easily.
Trick is to be careful, turn assists off (though ABS and skid are fine iirc) and turn in before you get to the corner to get a good drift going. The AI thinks it's on tarmac, just drive like you'd actually drive in a rallye and they're easy to beat.