Sliced cheese freezes and defrosts just fine. Block cheese once frozen/defrosted, tends to crumble when grated. If you want to freeze cheese that will eventually be used for shreds, shred first, then freeze. Shredded cheese defrosts faster, too. If you use ham with a high water content (typically the cheap stuff), it can result in doggy bread. Solution: use better ham or keep it frozen until right before consumption.
Related: I used to buy the Kirkland sliced turkey for DH's sammies, but it does the same watery thing upon defrosting. I bought the more expensive Columbo brand turkey when it was on sale, and absentmindedly froze the whole damn twin pack. To my surprise, it was fine when it defrosted. It costs a little bit more, but avoids waste. If DH has a few days off, I can toss the package in the freezer so it doesn't go bad. Totally random tip: if I'm not sure the meat is still good, I offer a tidbit to the cat. If she turns her nose up, I know it's too far gone. This is especially helpful since I'm a vegetarian. It is not cost effective to acquire a cat solely for this purpose, but if you happen to have one on hand...
Warning: Mayo does not freeze well. Butter or mustard are better choices for your frozen sammy experiment.