Ubuntu Snappy Core does not work on Raspberry Pi Zero, or for that matter on any ARMv6, such as most RPi models: 0,A,A+,B and B+. All of above are based on BCM2835/BCM2708 SoC.

UbuntuSC requires ARMv7 ISA CPU, which among Raspberry Pi models is only featured on the BCM2836/BCM2709 SoC in "Rasbperry Pi 2 Model B" (note the "2").