Is it a bad idea to express my personal feelings about the subject when writing email to a professor for PhD application?

To express that you are motivated is a good thing. The difficulty is getting the "tone" right. This is in part a cultural problem. If you are not German and you happen to know someone who is, then you could ask her or him to read your letter and see if you get the right message across. It would be even better if that person is also from the same discipline, as cultures also tend to differ between disciplines.

In general I would keep this part short and to the point. If you have a specific reason why this is your dream (and it is not too personal) than it might help to mention that.

Just having strong interest in a specific topic wouldn't justify your application in Germany. It is a norm in Germany that one's interest in a specific field is judged by his/her previous achievements in that particular field.
My sincere suggestion is that don't waste your precious space in the application letter/email, by boasting about the interest. Rather, try to sell your previous achievements.

Keep it short and to the point (following advice in similar questions on this site). In particular, since you want to move into a different (sub-)field, state the work you did in your current field (especially published work, if any), and point toward key courses you have taken that would be advantageous.

Say you did computer vision with a published paper, state that, but also state that you have taken courses in biology if you want to do a PhD in bioinformatics.

I wouldn't care that it is your 'dream', I suppose that every potential student is strongly motivated to do their PhD. So don't 'waste' precious space stating it.

(The last line is my personal opinion, obviously, but at least I'm german ;-) )