Druids solo capability is behind that of other tanks for sure, but you can do quite a bit of stuff. My experience is however its best to stay in bearform if you are unsure if you can manage the bosses damage. Healing won't do you much good, unless there are phases where the boss won't hit you because he's casting or theres some triggered event. If theres no danger of dying catform works well ofc.
Then its simple math. If iLotP and frenzy regen every 2 min can keep you up you can do it, otherwise its pretty much though luck.
I soloed all mount relevant bosses but Kael25 of the pre-WotLK content during WotLK, with 85 most level 60 stuff should be trivial and you can farm Skadi as well (don't call him until most of the adds are down ofc). When I went farming the red AQ40 mount I got up to the twins which I couldn't down obviously. At Skeram its all about killing the snake-adds in time, which can be tricky as you get stunned (webbed) a lot. I'll give MC a try when I feel like it, did it 2man at 80 for the rep.
If you are serious about soloing content you will find it easier to do with an DK or paladin (in that order, certain encounters might be easier with bear than pala, but thats a few), but it depends on what you want to do. A DK killed Kael25 for reference While I haven't tried him yet at 85 I don't see it being done with a bear anytime soon.
I don't have much to say about warrior soloing, thez changed quite a lot and I have yet to try it. I'd say it depends quite a lot on the boss - like if you can utilize spell reflect or your below 30% victory rush healing.