Either class has a chance, we won’t be in WotLK and above when Mages lose by default against hunters (at equal skill level, of course).
From what I remember as one who played a H in Classic throughout, it was easier for an undergeared Hunter to defeat a better-equipped Mage than vice-versa. But a caveat here: Hunters are really setting-dependent in Classic and you will have plenty of opportunities to catch them in tight spots, such as flag rooms.
Otherwise, however, rush forward. The following steps are quite likely.
1 If he’s good, he will force you to Blink to get in his DZ, even if you’re coming at him mounted. The H will save his Scatter Shot for Blink.
2 Now, some Hunters have SShot+Trap so ingrained into their brains, that some will actually FD, move in and lay it. If one does, it should be easy for you. Let him trap, Ice Block yourself out, then Frost Nova the H + pet before they gain distance. But a good H will simply SShot and move away, j-shotting you with Concussive as soon as the disorient ends.
3 So you have to IB the SShot and catch H + pet in Nova. Sheep the pet. The H will interrupt your first FB with FD. If H is NE, he will Shadowmeld as well, forcing you to come closer or use AoE, breaking him out of Nova.
From here it’s anyone’s game and it shouldn’t last until the H’s next SShot either way. 1 Iron Grenade or a net can win it or lose it for you.
P.S. Remember that even a Survival PvP H (with 5/5 Survivalist)
has access to Scatter.