Small neutral wire at service drop to panel
It is common in really old homes to find a #10 (10 gauge or AWG) wire for a 60-amp neutral.

However, it's underrated for today's more power-hungry world.  If I remember correctly (pros, correct me if I'm wrong), your house should have #6 wire for the two hot lines, #8 for the neutral, and #10 for the earth ground.

Are you at risk?  A pro would be forced by code to tell you yes, but it really depends on what you're operating.  There is no simple "rule of thumb" that will tell you if you're OK, thus the need for the pros (and the reason the code changed over the decades).

A simple test is to touch the insulated neutral when you have a high-average amount of power being consumed (dryer's running, stove's on, TVs &amp; computers are operating, and the lights are on type of thing).  If the wire is warm, you have risk.  If it's not, you're OK (with the caveat that this is a simple test and can only be trusted to a degree).

Please be careful touching that wire.  Don't get shocked.  Your safety is more imporant than a simple test.  If you can't easily touch the wire without risking shock, call an electrician!