How can I get off dots of white spray paint without damaging the leather of my black tall boots?

Try black shoe polish
It depends on the type of paint... please tell me it's white leg "paint".. which is water based, and saddle soap and warm water will take care of it. (Followed by a quality conditioner) If it's an oil based spray paint (something you'd need a paint stripper for) some very careful spot cleaning with WD-40 or Brake Cleaner might work. As a previous answer mentioned--- spot test first! Follow with a quality conditioner, regardless. Good Luck!! ☺
Olive oil might be able to lift the paint whilst helping the leather. Vaseline (petroleum jelly) might also work.

If they don't work, a little bit of nail polish remover on a cotton earbud shouldn't do too much damage to the leather unless it super cheap leather.

Always spot test first though!
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