What problems would the early F-16 have if they were to fight during night?
When the LWF program began, its founders envisioned an aircraft purebred to engage the Soviet threat with machines which more closely matched the majority of Soviet fighters at that time ie lightweight, very maneuverable day fighters ie equipped with minimal avionics, a cannon(s) and short range IR guided missiles.  Pierre Sprey had envisioned an even smaller fighter when he didn’t even have a fire control radar in it, but it was not developed past his proposal.

The prototype and development F-16s were a far cry from a modern Block 60+ F-16 is today in terms of avionics and capabilities, but the first service F-16, the Block 15 F-16A/B, had good day and night air-to-air capabilities with the APG-66 radars.  They were however limited to good weather air-to-ground operations as they were limited in their precision munitions delivery capability.

Upgrades over the next three decades of service led to the current incarnations of the Viper equipped with helmet mounted cueing systems, advanced fire control AESA radar sets, IR night and precision weapons targeting systems, BVR TARH capable air to air missiles, advanced glass cockpit displays, etc.  It must also be noted that, while these system offer addition capabilities, the added weight and complexity diminishes aircraft performance in traditional fighter metrics as well.  Nevertheless the F-16 still remains a fine fighter regardless.

The capability vs cost vs performance debate is always controversial and does not show any signs of ending soon, though the military seems to prefer the most advanced and capable hardware it can buy at the expense of operating costs and reliability.  This has been made painfully clear with the F-35 program.