There is no report in the Sunnah that the Prophet (blessings and peace of Allah be upon him) did not pray Jumu‘ah because of rain or snow; rather he did not pray it when travelling.
It is permissible to not pray Jumu‘ah and prayers in congregation in the event of heavy rain, cold wind or snow which is bothersome to people and makes it difficult for them to go to Jumu‘ah, because of the report narrated by al-Bukhaari (901) and Muslim, according to which Ibn ‘Abbaas (ra) said to his muezzin on a rainy day: When you say Ashhadu anna Muhammadan Rasool-Allaah, do not say, Hayya ‘ala al-salaah (come to prayer); rather say, Sallu fi buyootikum (pray in your houses). It was as if the people found that objectionable. He said: One who is better than me did that. Jumu‘ah is obligatory, but I did not want to force you to walk in the mud and on slippery ground.
[al-Nawawi] said: This hadeeth indicates that Jumu‘ah may be waived because of rain and the like. This is our view and the view of others. Something different was narrated from Maalik (may Allah have mercy on him). And Allaah knows best which is correct. End quote.
The Hanbalis regarded snow as one of the reasons that make it permissible not to go to Jumu‘ah or prayers in congregation.
Its says in Kashshaaf al-Qinaa‘ (1/495): Attendance at Jumu‘ah or prayers in congregation may be waived in the event of rain, mud, snow, ice or a cold wind on a dark night, because of the words of Ibn ‘Umar: The Prophet (blessings and peace of Allah be upon him) would ask his caller to call out on a cold or rainy night when travelling: Pray where you are. Agreed upon. It was also narrated from Ibn Maajah with a saheeh isnaad, but he did not say “when travelling.” In al-Saheehayn it was narrated from Ibn ‘Abbaas that he said to his muezzin on a rainy day -- Muslim added that it was a Friday -- … and he narrated the hadeeth quoted above. And the same applies to snow, ice and cold.
This confirms that cold wind on a dark night is an excuse, because it is likely that it will rain. End quote.
It is well known that many people are not bothered by snow and it does not prevent them from going to work and meeting other needs. For these people, snow is no excuse for them not to attend Jumu‘ah. But if it bothers them and makes it very hard for them to get to the mosque, then it is an excuse.
And Allah knows best.