The first thing you may notice if you're talking about or reading about the weather is that the verb hacer, which in other contexts usually is translated as "to do" or "to make," is frequently used to discuss the weather. Here are a few examples: ¿Que tiempo hace? How's the weather? Hace sol. (It's sunny.) Hace mal tiempo. (The weather's awful.)
In English, it is very common to use "it" when discussing the weather, as in the sentence "it is raining." In Spanish, it isn't necessary to translate the "it": Use either the hacer form explained above or the third-person noun without a subject: Nieva. (It's snowing.) Nevó. (It snowed.)
Most textbooks advise against using sentences such as es frío to say "it's cold," and some say that such a usage of the verb ser is incorrect. However, such expressions are heard in informal speech in some areas.
When discussing how the weather feels, use tener, which usually is translated as "to have" but in this context is used to indicate how a person feels. Tengo frío. (I'm cold.) Tengo calor. (It feels hot.) Something to avoid is saying something like estoy caliente or estoy frío for "I'm hot" or "I'm cold." These sentences can have strong sexual overtones, just as do the English sentences "I'm hot" (in some contexts) or "I'm frigid."
Once you get beyond the basics, here is a vocabulary list that should cover most situations or help you understand the forecasts you'll find online or in newspapers:
altamente highly
aviso advisory
calor hot
centímetro centimeter
chaparrón downpour
chubasco squall, downpour
ciclón cyclone
desconocido unknown
disperso scattered
despejado cloudless
este east
fresco cool
frío cold
granizada hailstorm
granizo hail, sleet
huracán hurricane
kilómetro kilometer
humedad humidity
leve light
lluvia rain
mapa map
mayormente mostly
metro meter
milla mile
mínimo minimum
nieve snow
norte north
nublado cloudy
occidente west
oeste west
oriente east
parcialmente partly
pie foot
poniente west
posibilidad possibility
precipitación precipitation
presión air pressure
pronóstico forecast
pulgada inch
rocío dew
satélite satellite
sol sun
sur south
temperatura temperature
tiempo weather, time
ventisca snowstorm
visibilidad visibility
viento wind
vientos helados wind chill

