We investigate the magnetotransport properties of connected kagome artificial spin ice networks composed of permalloy nanowires. Our data show clear evidence of magnetic switching among the wires, both in the longitudinal and transverse magnetoresistance. An unusual asymmetry with field sweep direction appears at temperatures below about 20 K that appears to be associated with exchange bias resulting from surface oxidation of permalloy, and which disappears in alumina-capped samples. These results demonstrate that exchange bias is a phenomenon that must be considered in understanding the physics of such artificial spin ice systems, and that opens up new possibilities for their control.