Will uncooked meat tenderise or toughen while stored in a refrigerator?

While dry aging does impact texture, storing a portion that you might purchase for yourself, or a small number of people, in the refrigerator for a few days will not impact the final texture. Instead, consider purchasing high quality cuts, and the correct cut for your application. Consider a tenderizing pre-treatment (some marinades are intended for tenderization). Finally, of course, cooking process will greatly impact the final texture.

This depends on many factors. From what I've seen, meat tenderness vs. toughness depends mainly on the amount of shock you create when cooking it.

The main effects I've observed:

• if you put the super-cold meat from the refrigerator right on the pan, the shocked proteins (esp. long keratin fibers) are going to shrink, causing the steak to became super compressed and tough as a result. This doesn't happen (too much) if your meat is room-temperature before cooking it.
• you can prepare the meat chemically to withstand this shock better. E.g., add salt a few hours earlier (even in the refrigerator) to avoid a brutal ion gradient passing through your steak when cooked right after being salted, again shocking the protein
• technically, storing the meat in the right conditions (relatively dry and cold) lets the protein slowly degrade and make it respond less, thus making the result less tough again.

How long it is stored in the freezer alone, i.e. without any kind of marinade, and with no biological protein degradation process going on (as with dry aging), should not generally matter. At least until your meat gets spoiled.

Extras:

• tenderizer tools work by breaking much of the "long" protein chains, thus making this shrinking shock less prominent in the result

• non-pH-neutral ingredients (lemon, milk, youghurts,...) are a great way to reduce the shock chemically