Anyway, you had better NOT use too many words with "ぽい" when you have to speak formally. If you spoke that way, they might think you to be "学生っぽい", "子供っぽい", or even "馬鹿っぽい" in the worst case.

Compared with "らしい" and "みたい", "ぽい" is more difficult to use properly. ／It is mostly used in casual conversations with your family and friend, especially when you talk with them about fashion like ""男っぽい (manly, mannish, masculine, etc) ", "女っぽい (womanly, feminine, etc) ", "子供っぽい (childish) ", "少女っぽい (girlish)", and so on.／ You usually say "ＡはＢっぽい" if Ａ is NOT Ｂ as in your second sentence. ／ There, your mother is NOT a child. Even though, she wears childish clothes. ／ In some case, however, you could say "ＡはＢっぽい" even if Ａ is Ｂ. ／e.g. "彼女はいつも女っぽい服を着ている"（You could say this way because most women often wear mannish clothes too, though I would say "女らしい服を着ている". ／ On the other hand, "あの子供はいつも子供っぽい服を着ている" would sound a bit weird probably because most children quite naturally wear childish clothes, which is NOT worth commenting on, as in the "冬なのに・・・冬みたい" case I have just explained.

On the other hand, "みたい" means "like". You can say "ＡはＢみたい" only if Ａ is NOT Ｂ. ／ In your first sentence, "冬なのに・・・春みたい" does make sense because 冬 is NOT 春. In this case, however, "冬なのに・・・冬みたい"（Ａ＝Ｂ）would sound weird because it is quite natural and not worth commenting on. ／ In your second sentence, you could say "母は子供みたいな服を着ている" because 母 is NOT 子供. （"子供っぽい" would be more natural, though.）

”らしい” means "typical of", "suitable for", "becoming to", or something like that. You can say "ＡはＢらしい" only if Ａ is Ｂ. ／ In your first sentence, you cannot use "らしい" because "winter" is NOT "spring". "冬なのに春らしい" doesn't make sense at all. ／ In your second sentence, you cannot use "らしい" either because "mother" is NOT "child". "母 (大人) が子供らしい服を着る" doesn't make sense at all either.