Cerebellar climbing-fiber-mediated complex spikes originate from neurons in the inferior olive (IO), are critical for motor coordination, and are central to theories of cerebellar learning. Hyperpolarization-activated cyclic-nucleotide-gated (HCN) channels expressed by IO neurons have been considered as pacemaker currents important for oscillatory and resonant dynamics. Here, we demonstrate that in vitro, network actions of HCN1 channels enable bidirectional glutamatergic synaptic responses, while local actions of HCN1 channels determine the timing and waveform of synaptically driven action potentials. These roles are distinct from, and may complement, proposed pacemaker functions of HCN channels. We find that in behaving animals HCN1 channels reduce variability in the timing of cerebellar complex spikes, which serve as a readout of IO spiking. Our results suggest that spatially distributed actions of HCN1 channels enable the IO to implement network-wide rules for synaptic integration that modulate the timing of cerebellar climbing fiber signals.