Should I not use a trail because of poor conditions? I spoke with someone and they said they were staying off certain trails because snow melt and mud would ruin the trails.  I had never thought of this and really want to be considerate.

Is this a valid concern?  Should I avoid a trail because of this?  How do I know when it is ok to use?
It's common etiquette, at least everywhere I've been, to stay away from wet and muddy trails (unless they're supposed to be or always are a mudfest). Riding on a muddy trail makes ruts which make the trail conditions worse for everyone once the mud dries and the ground hardens.

In addition to ruts, if the trail is muddy and you slide out a front wheel going around a turn, for example, your wheel can scrape several inches of trail off. This can cause erosion problems later on.

However, as alluded to earlier, if the trail is a known mudbog and stays muddy year-round, one more rut probably won't hurt anything.

Another common counterexample is when the trail is melting in the afternoons but can be ridden early in the day when the ground is frozen. If you're crazy enough to be out riding then, more power to you.

But generally speaking, it is in good taste to stay off melting, muddy trails. Any time your presence can alter the trail physically (ruts, slide-offs, feature damage), everyone else who shares the trail with you will be glad you stayed off.