As a Hunter player, what race you choose is going to be your single most important choice when it comes to your Hunter build. No one race is better than another. Each has its own pro's and con's and as such you should choose a race which will fit more to your playing preference and cosmetic choice (the way you want your hunter to look). As a Hunter you have five choices to choose from. From the Alliance you have Dwarves and Night Elves. For the Horde you have Trolls, Orc's and Tauren. We think it's important to note at this point that later on down the road, there is very little difference between any of the five. Your major pro's and con's are going to stem from your talent choices and the gear that you have on your character. But in the beginning game race does play a role.
   As for the Alliance, there is one major difference. Dwarves start out with a much higher amount of hit points and Elves start out with a much higher percentage of dodge (that's in addition to the +1% they get as a racial benefit). What does that mean? That means that dwarves can take more of a beating, which is nice since you don't actually get your pet until level 10, and Elves get hit less often then dwarves do. In the end it all evens out, but that is pretty much the only major difference between the two. 
   On the hand, Dwarves have a racially innate talent with Guns (+5 bonuses) which pretty much makes them one level higher then other hunters in respect to their skill with their ranged weaponry. Once again, in the lower levels (prior to 30) this is going to give you a slight advantage. But it really won't make much difference when you hit the end-game in the long run.
On the other hand, Elves lack this inherent bonus get a nifty little trick which is unavailable to Dwarves and which we find quite invaluable given the right situation. Elves can stealth, albeit a stationary stealth. It means that they can't move at all. But this ability is quite nice if you're going AFK for a few moments and don't feel like getting ganked by a passing mob or Horde opponent. If you're setting yourself up into a nice sniping position, Stationary stealth is the best sort of camoflage you need to prevent from being noticed from a distance. Now this stealth! In comparison to that of a Rogue, pretty much anyone who passes within melee range of you will discover you sitting there all by your lonesome. But, considering its a free ability, you can't really complain.
It draws a conclusion that Dwarves have a nice tracking ability which allows them to spot treasure chests on their overhead minimap. Not in itself a very Hunter oriented ability but it's just a nice little bonus. But Dwarves receive a stone-form ability which gives them some nice immunity at the cost of speed. It is important for you to have a nice little ability when put in a bind. For instance if your pet drops aggro and you're stuck melee'ing the beast. But those are the differences between the two. You also have their resistance bonuses. Elves get a +10 nature resistance while Dwarves get a +10 frost resistance. Basically Elves are better off against Druids and Dwarves are better off against frost spec'd Mages. That's pretty much what it boils down to.