The Senju are the descendants of Asura who did inherit Rikudou's Yang Release or Physical Energy which is associated with their life-force, so the Senju did inherit a very high life-force. I also don't know where you got the idea that Mokuton is a Senju power when none of the Senju bar Hashirama even possesses Mokuton meaning it's only an ability exclusive to Hashirama.
Hagoromo stated Ashura inherited his body, the Sage's body was the body of a Juubi Jinchuuriki. Mokuton was exclusive to Hashi because he was Ashura's transmigrant, likewise Naruto's use of bijuu chakra was exclusive to him because he was a transmigrant.
In other words, Mokuton is a Senju KKG but only a transmigrant can unlock it because it's essentially the Juubi's power, Naruto's ability to use bijuu chakra is on par with the Gedo but only a transmigrant can do it because it requires the Sage's body.
So basically the Juubi Jinchuuriki's body was inherited by Ashura and then divided into two clans. Senju = Juubi - Uzumaki = Jinchuuriki
Regarding the life force, it was already stated that life force was an Uzumaki trait, the red hair was the sign of strong life force, imo Senju inherited talent for elements because Tobirama was known as the best Suiton user, Hashi had an affinity for all basic elements and Mokuton is considered the highest form of element manipulation after TSB.