Should the Hare nap when in the lead among remaining racers?
While you are right that the hare moves more frequently than the other animals, its up to the players not betting on the hare to win to make sure to not let someone just play 1 card per turn, (as this would be the most effective way to win with the hare). If you are playing with new people you will see that this is a clear tale on when someone is betting on the hare.
Usually when this happen all the players not betting on the hare(assuming there is no other player betting on it) can easily horde hare cards and only play them when there will 4 on the board, or when a howl is played.

If no one has willingly picked the hare the game has a total of 76 cards(since each player bets 5 cards out of the deck), and out of those 18 are hare.  Now each player holds 6 cards so the chances that a player has a hare card is 23% this is almost guarantees that the non betting players will have a combined total of 4 hare cards. Since they aren't betting on the hare to win then if played correctly they should be able to throw away 4 cards at least in one turn. Combined with the howling wolfs cards this means that you can at least throw away 7 cards at minimum.

If you assume all players are betting on the hare (including the guy who is dealt the hare) the card total goes from 18 to 13. The more ppl bet on the same animal the less chance that animal has to win statistically, but since more ppl are going for it, it will most likely move more often. (If everyone is going for the hare no one will play more than one hare per turn as there is no benefit). 

Overall the game is very well balanced i have played this game probably over 200 times now, (this is a great game to play with anyone, and my friends and family love playing this game for how simple it is to pick up but how hard it is to master) and the outcome of the game now comes down to being able to read what each person is betting on.

Opps forgot to copy and paste the paragraph on answering the question, I interpret the rules as only when the hare is First place (or tie since technically they are tie for first place), so how can the hare be in first place if someone already won the race, and you are racing for second, and third? This is my interpretation and I have found out that this does not make the hare place second automatically. I would not make the hare sleep as I feel that it would significantly lower its chances of even placing at all.

As I pointed out earlier its fairly easy at the beginning to tell what people are betting on if they do the optimal play every turn so this game starts turning more into a meta game of how people play rather than people doing the optimal play because when you end up losing 4 cards of your animal it becomes basically impossible to win. 

I would most more statistics on the game but I'm at work currently and this response has gone on longer than it should already(I will try to update it with more numbers on how things play out assuming you have 5 players because with less players the game starts to become more about getting lucky to draw the right cards at the right time).