They can write all they want. The fact is, the countries wouldn't cant get rid of their farm policies because of voting. And the EU, is an outgrowth of those already existing countries. EU policy is not handed down from a white tower. Of course you can't actually say that.
Farmers and people supporting farmers are still a small minority and while they can probably swing some election in some country if they were to massively support only one party or coalition, the money comes for the strategic importance. It would be naive to think it's just "for the votes".
It was a long time ago that I have looked into this. My understanding from the political science is that countries where farmers votes aren't as important, also have far less subsidizes.
Groups that already have subsidizes are better at defending them. Even if in absolute terms their numbers aren't as big.
They are totally going to defend themselves, mainly through boycotts, barricades and varying degrees of riots. That can totally cause a vote issue, but it's because the rest of the population is pissed off by the road blocks etc