Here's my opinion on this:
I assume "Follow your dreams" is, ultimately, just yet another variant of saying "You can do anything if you really want it and work really really hard for it".
Humans have a tendency to blame failures exclusively on others - but to ascribe successes exclusively to themselves. (Both is equally far from the truth btw.) For example, there was an interesting study where someone made interviews with millionaires. Interestingly, every single one of these rich people believed that they were rich because they deserved it - and it didn't make any difference if that person was a selfmade-millionaire who earned it through hard work, became rich via inheritance, or simply won in the lottery...
Anyway, it is because humans tend to ascribe successes exclusively to themselves that such "follow your dreams"-phrases are usually uttered by people on a peak of success (like, as you mentioned, an actor who has just been given an award): At first sight, it seems as if a caring person is giving a good advice to others; but in a way, that person is pretty much just saying: "I'm very proud, this is a great success, and I earned it all by myself because I'm so great. I heard you're not as successful as I currently am - what the hell is wrong with you?"