What I don't understand is, which actor executes the color kernel?
Well, the point of executing color kernel is to find colorvalues... So each actor which is interested in finding colorvalues need to execute it, unless it can get colorvalues from trusted source. (E.g. via a cryptographic proof of some sort.)
Do you envision the miners executing the color kernel?
No, I see colored coins as an alternative to protocol changes. Having something on protocol level definitely has benefits, e.g. SPV (thin clients need very little information to verify payment), but it might be problematic:
1. hard fork is required (likely)
2. a problem in additional features might lead to consensus problems
3. changes are not compartmentalized
4. it's hard to add features, upgrade over time, etc. (again, hard fork is required)
But that's the theory... In practice, if you care about things like user currencies, securities and so on, they aren't that hard to implement, so a Bitcoin protocol upgrade (such as Freimarkets) is desirable.
Would that need an upgrade of the entire bitcoin network?
Yes... It is known as 'hard fork'.
Will wallets with the recepient address execute the color kernel?
Yes... Basically, when you see an incoming UTXO, you want to know its colorvalue, so you run the computation... But there are several different computation strategies, like pre-computing everything, or computing on demand only.