YES .. Peppermint uses the same default setting for the Ubiquity installers "Minimum Disk Size Requirement" as Ubuntu 12.04 (4.4GB IIRC) .. even though Peppermint is much smaller.
So even though Peppermint will easily fit on a 4GB drive, the Ubiquity installer will say your drive doesn't meet the necessary required size
So we need to change that "required size"..
Boot to the LiveCD/LveUSB .. once at the desktop, hit Ctrl+Alt+T to open a terminal, and run:
sudo gedit /usr/lib/ubiquity/ubiquity/misc.py
Line 796 (very near the bottom) will read:- min_disk_size = size * 2 # fudge factor.
Change that to read:- min_disk_size = size * 1.4 # fudge factor.
SAVE the file.
Now run the installer from the "Install Peppermint" icon on the desktop.
Ubiquity will now state that it requires a 3.1GB drive
BTW .. DON'T install Peppermint with the SD card inserted
.. only insert the SDcard AFTER installation.