The location is very important:

... what Pokémon you can encounter depends largely on your location. Walk near a beach, and you’ll find more Water types, for example.

(from here)

I cannot find anything that relates weather to the Pokemon types. I don't think it is an influence factor.

I think you will find this link helpful: http://www.pokemongodb.net/2016/04/pokemon-go-types.html

It has a chart at the top showing what percentage of Kanto pokemon belong in each type. Below, it shows a list of all Pokemon in the game and after that there is a chart showing what type of Pokemon to expect in various Biomes.

Happy Hunting!

Possible Types

Normal

Boundaries, Landuse, Places, Roads, Transit, College, Commercial, Common, Footway, Hospital, Hotel, Library, Major Road, Minor Road, Pedestrian, Pitch, Playa, Recreation Area, Retail, Runway, School, Sports Center, Stadium, University

Grass

Landmass, Farm, Farmland, Farmyard, Forest, Garden, Golf Course, Grass, Meadow, Nature Reserve, Park, Path, Playground, Residential, Wood

Bug

Farm, Farmland, Farmyard, Forest, Garden, Golf Course, Grass, Nature Reserve, Park, Path, Playground, Wood

Water

Water, Basin, Canal, Dock, Drain, Glacier, Lake, Ocean, Reservoir, River, Riverbank, Stream

Flying

Farm, Farmland, Farmyard, Forest, Garden, Grass, Nature Reserve, Park, Wood

Rock

Building, Landmass, Highway, Industrial, Parking, Quarry, Railway, Urban Area

Ground

Landmass, Ditch, Land, Parking, Playground, Railway, Taxiway, Urban Area

Fairy

POIs, Cemetery, Place of Worship

Dark

Cemetery, Cinema, Theatre

Steel

Building, Railway

Dragon

POIs

Ghost

Cemetery

Ice

Glacier

Psychic

Hospital?

Electric

Industrial

Fire

Residential?

Poison

Wetland