Snow fell throughout the opening 45-minutes and needed to be cleared during an extended half-time break, by which time Pep Guardiola’s side were a goal to the good thanks to Ilkay Gundogan’s close range finish.
Substitute Fernandinho added a deserved second from the edge of the area, before Manuel Lanzini struck a wonderful consolation for the visitors in the final seconds.
City were on top for much of the game, but were forced to work hard against the in form Hammers and Rodrigo was pleased with the character shown by the hosts.
"Today was a battle on the pitch," he said. "It was a difficult day due to the weather conditions.
"But of course, it is always difficult against this team, they one of the toughest in the league.
"They can punish you on the counter attack. They are players you have to control more.
"It wasn’t good for us due to the weather so it was tough. In the first half we couldn’t play much, it was more long balls because of the weather.
"In the second half we dominated more and created more chances. It’s a good victory for us."
The Spaniard was a typically reliable presence in the heart of City's midfield, breaking up play and providing the platform for the team to attack.
The 25-year-old has been in fine form this season, but on a day when several key players were missing, he was keen to highlight the contribution of the whole squad.
"This is all about the team, all 24 players we have in the squad," he added.
"We all need to be involved. Everyone is going to be important.
"People who maybe weren’t involved as much early in the season are now taking the responsibility.
"We have key players out, but we’re still winning and playing well - that’s the key to success at the end of the season."