1) Is it a must to recite Quran loudly or we can recite in our heart?
2) In winters can we wipe/dry our hands after wazoo

1) It's necessary to recite Quran at least in a way that the holy words of Quran must be pronounced and the volume of voice should be so much high that the reciter can hear himself his words otherwise it will not be considered recitation "qera'at" as this is very obvious by the word recitation itself. So if a person wants to take the reward of recitation he must recite it by vocal expressions not only in heart but if a person just recites the verses in heart he will get the reward of looking toward Quran or memoirizing it.
2) We can wipe/dry our face and hands after wuzoo in any season including winter but it's famous among Jurists that this is makruh. Therefore almost all foqaha consider it makruh except a few maraje like Ayatollah khamenai says that if a person keeps a special towel for drying the water of wuzoo then it is permissible.