For a while their was a fierce rivalry: the Bears took the facility's but lost one of their most favorite and best Khans. The next dozen years until Horse Khan Fletcher's death was the Horses being ultra radical and Crusader with a hatred of the Ghost Bears as a focus. The Bears disliked the Horses and sought to uphold their position in the Inner Sphere and as Wardens against what is most likely their direct competitor in terms of tactics and strategy: i.e. Elementals, combined arms, etc.
After Khan Fletcher's death things scaled down slightly: grudges were settled. The Trial for Jake Kabrinski and the taking of an Occupation Zone in the Inner Sphere by the Horses sorta settled into a Cold War-ish scenario. Mutual respect, some cooperation against the Blakists, and Jake Kabrinski rising to Khan didn't hurt either. Not as great allies as the Snow Ravens or even the Diamond Sharks but not quite enemies anymore.
Fast forward to the Dark Age and Malvinas Horses have sunk their teeth into the Horses. A mini-civil War has split the Horses into two factions both seeking to supplant the other has gripped the Horses and their common foil is the Ghost Bears. The Wolves have moved out and the Falcons are 'allies' so let's pit our forces versus the Bears. Cooperation is no longer a thing, and the Bears might have the flex their muscles to show them why you shouldn't mess with the Bears. Skirmishes have been frequent to say the least and both sides have come out even, but the old saying goes (especially in BT) 'Don't poke the sleeping bear'.
Just my two cents and opinions.