Interface down alarms are Major by default, not critical. You probably don't want to filter all link-down alarms though. You probably want to change your system settings to filter alarms for access ports.
Cold start is usually something people are worried about - unexpected device reboots are generally bad. If a device has a short reboot cycle, it's possible that the polling window will miss a short reboot. Cold start traps will alert you that something happened.
You can change the severity by going to Alarm -> Trap Management -> Trap Definition.
Search for the alarm you want, and change the severity.