Shrinking Cubase Objects on Large Monitor

HDMI can pass anything that DVI can. HDMI is DVI (except that HDMI has an extra pin for audio transmission).
Problem with that is that the higher resolution you go, the more data needs to be sent at once.
Larger displays (as well as 120 Hz LCDs) have to use dual-link DVI connections. HDMI (except for 3D ready systems) is only single-link.
I think display port solves this, but it’s usually only on higher-end displays.

Most video card’s HDMI outputs only output by default the “video” resolutions (480p, 720p, 1080p).
The driver can be tricked into outputting “computer” resolutions over HDMI. As stated above, it is technically possible.

Yes, I’m fine with that.

Thanks, Shinta,
You’re helping to clear my understanding on the issue.

Your TV is going to have it’s limitations too.

It probably won’t take any signal above 1920x1080 (1080p).

It just won’t show anything (other than a “default” screen).

You don’t think so, eh? Even if I use a DVI input?

No.
Your TV’s processing engine won’t know what to do with the resolution, so it’ll say “unknown resolution” or something along those lines.
Most computer monitors today are like that as well.