Why does 03 Beetle -2.0 gas- not start on cold mornings below 32- Just a small click when you turn the key- Always starts when warmer or if able to park in garage overnight?

Ur battery cable may need to be cleaned coz battery acid corrodes on cables & its not getting a good connection. If theres no corrosion on cables then the cables may b loose. If its still having hard time cranking then it may need a new battery...possibly a stronger battery..