I am a Linux newbie, and I am trying to dual boot Linux Mint with Windows 7. Right now, Windows 7 boots from a small SSD, which has little extra room on it. Is there a way to set up a dual boot where I can put my Linux files on my larger HDD, without completely redoing my drives? For example, could I put the bootloader on the SSD and have it load an OS on the HDD? How would I do this?
Yes (although I haven't used Mint - this answer is based on Fedora and Ubuntu, both of which I've done it with).
During the install you are asked which partitions to install the OS onto, these can be specified on any suitable and connected drive.
As another part of the install (usually after the partitioning choices) you are asked where to install the bootloader.
If you choose to install this on the boot sector of the primary drive (the SSD in your case). Hopefully (and I'm saying hopefully because I don't know how Mint works precisely) your existing Windows OS will be detected and provided as an option in the bootloader along with the Linux install on your second drive.
Word of caution - once you have everything setup on two drives removing or changing either of them will break booting because:
Check what method is used for booting - if the system is able to use UEFI and Windows is set up to use it, you can add Linux as another option rather easily, because the disk already carries a special EFI partition used for booting. See e.g. tutorials on Linux mint sites: e.g. How to install Linux on UEFI systems where GRUB fail to install? or UEFI Install dual-boot.