As well as warmth, boots and gloves also offer protection from poorly maintained dive boats in the tropics, sharp edges on wrecks and offer grip when scrambling over rocks on the shoreline.
A good pair of dive boots will fit snuggly but not squash your toes and provide protection between your foot and fin. The hard sole will also offer your feet protection and grip while walking around boat decks or shore diving.
Gloves have many uses, from thin 1.5mm for protection against sharp wrecks in the tropics to thick 7mm gloves to give maximum thermal protection in the coldest of waters. Just remember the thicker the glove the less dexterity you will have so it’s a fine line between movement and warmth.