Weather to expect in Seville
Heat
The one thing you likely know, or should know, is that it gets really, really hot in the summer. I mean it's damn hot in the summer in Sevilla, especially in August. Sevilla holds the record for the hottest city in Europe with a record of 50° C (122° F). That was back in 1888, but I do believe they tied or broke that in August of 2003, when the temperature in the street rose to 52° C, or 126° F! On those days the streets were literally empty during the middle of the day. If you wanted to go out you did so before 10am and then not until maybe 11pm at night. Friends of mine with little food in the house preferred to stay inside and be hungry rather than brave the heat.
Cold
In the winter the temperature will almost never break the freezing mark and so things are relatively mild. There are many houses which do not have heat and as marble floors are common it can be much colder inside. So it's not likely you'll need that heavy winter coat, but layers do help and slippers are a must.
Rain
Rain is uncommon if non-existent in the summer months of July and August. In 2003 we went almost 4 months without any significant rainfall. In October the rainy season begins and lasts through December. In March it picks up a little and then starts a downward trend. And while I know it differs from my chart below, I swear October is often the poorest month for rain in Sevilla. If your looking for snow head to the Sierra Nevadas outside of Granada, as the last time it snowed in Sevilla is at least 50 years ago. I saw a picture from that year somewhere with snow in the Plaza de la Encarnación.