Okay this is interesting. Once you get Shadowmere, you have a constant companion. Period. Fast travel anywhere, Shadowmere is there whether you want him/her there or not. And, after doing an assassination Shadowmere will attack the guards if the assassination is in the same area like the one in Ivarstaad. YOU will not accrue bounty in the region. You will notice your total bounty going up, but it will not say WHERE your bounty went up, like it does when you attack a guard. You can walk right up in the fray, the guards will not attack you. You can hop on Shadowmere, and ride off. They will fire arrows at Shadowmere, and the guards will show up as your enemies, but you're not the target.
This is weird. I guess you're joined at the hip, but different.
Anyone else notice this? or is this a bug? or is this the way horses behave? or am I just noticing this because Shadowmere actually survives these encounters.