To cross-compile a program on a PC you must have the development files for the same packages installed on the PC as the ARM target. Qt 4.8 depends on OpenSSL, so you must get the correct development files for the ARM release if you wish to compile Qt.
- Install a Ubuntu 12.04 PC virtual box. SAME VERSION as the board.
- Get the compiler.
apt-get install arm-linux-gnueabihf
(You knew that). - Get required development packages.
apt-get install libssl-dev
or
apt-get build-dep -aarmhf qt4
(which only works for X11). - Edit your Qt configuration to suit your needs and build it.
The current step you are missing is step 3; but to perform it you need step 1 or some other way to get the OpenSSL development files for Ubuntu 12.04. There is probably some other way to do this using apt.sources. I think the steps above will be easiest for you.