It's true, some lactose intolerant people have the problem no matter which animal's milk it is, while others only have it with cow's milk (dairy allergies are the same way). But if you (martha) were able to drink water buffalo milk with no ill effects other than disliking the taste, then that's *probably* a sign that you're only intolerant of cow's milk.
I don't drink water buffalo milk when I'm in India (or anywhere), because I discovered the hard way from trying raita made with it that I'm allergic to it too. But the only complaint I've personally heard from travelers to India before this is that it was a bit too rich for them. I wonder if maybe the milk you were drinking was simply poor quality--subpar fodder and/or sanitation will make any milk taste bad, and dairy production in India is very decentralized, which can easily lead to quality control issues if the co-op system of the state in question doesn't have its act together. There are subtle differences between the tastes of various common animal milks, but if it's hit-you-over-the-head-grossout different, then that's almost certainly a problem with the production rather than the intrinsic qualities of the milk. Still, personal expectations are a big factor in whether something tastes good, especially when you're talking flavor combinations--for instance, I've heard more than one person say they enjoy drinking goat's milk straight for variety, but when they try putting it on cereal, the result somehow doesn't "taste right." Which is why I was thinking it might be good if ice cream flavors that goat's milk is known for having a natural affinity for were available.
There are commercial coconut-milk-based ice creams out there, too, so if you decide you don't like the goat's milk variety and want to try a non-soy vegan alternative, you might give that a shot, assuming you like the flavor of coconut.