We always played as the player who wins the hand when I was a kid, but we used the Penguin Encyclopedia of card games as our rules reference so that's not an independent source. It's meant to be an advantage - It's a prize for winning the hand (as opposed to the other thing of not being eliminated by taking zero tricks)
Don't you find that too strong? The player who wins the previous hand already has the reward and even bigger advantage of calling trump. Leading the first trick also offers some advantage, so I'd be inclined to think the game becomes too unbalanced if both advantages are given to the same player.
We normally play with the lead given to the person on the left of the player who called trump. The Penguin Encyclopedia seems alone in giving the lead to the player who called trump; most other authorities seem to have the lead rotate around the table.