Spain in February or March - good idea or bad?

Why not go? Anytime is good. Just prepare appropriately for the weather.
February 26 through March 9 would be best giving you 11 nights in Spain, I think.
Are the flights in and out of Madrid ??
Fly in to Madrid then AVE train to Cordoba (2 nts)
AVE train to Sevilla (3 nts)
Train to Granada (2 nts)
Train to Madrid (4 nts)

Unfortunately, we would only have 8 nights. Yes, I was thinking in and out of Madrid, it gives us the best flight times. I was tentatively thinking:

Seville (4 nts)
Granada (2 nts)
Madrid (2 nts)

I know Madrid is cut short but I figure it won't be the only time we ever visit Madrid. I was thinking a day trip to Cordoba from Seville.

Sounds like you are on the money. Go for it !!
Remember February has 29 days next year - a 3rd night in Madrid would be good.

If you want to start in Seville, see if you can get a flight into Seville and out of Madrid for the same price as a round trip to Madrid. To find these flights, use the "multi city" option on booking sites. Don't look for 2 one-way flights, as that's usually much more expensive.

You will have to change planes in Madrid (if not somewhere else) to get to Seville, but it's easier to change planes than to get into central Madrid to take the train. It's can also be cheaper in the end (even if the flight ticket costs more), because you probably don't want to have a non-refundable train ticket on your flight arrival day (risky, since there are many variables that could cause you to miss that train). So, you're looking at a full fare train ticket from Madrid to Seville - about €75.

Great idea. I went in February 2013 and had sunny pleasant weather for 3 solid weeks in Andalusia, chilly and drizzle in Madrid for 2 days. I went back this year, again in February, for a week in Andalusia and a few days in Madrid and Toledo. Mostly great weather again, with a couple drizzling cloudy days in the middle. By warm I mean short sleeves and cold drinks temps. I'd planned a day trip from Madrid to Segovia, but snow was forecasted there so I stayed in Madrid and only needed a light jacket.

We were just in Spain the part of the first/second weeks of March this year, and the weather, lack of crowds, etc. was absolutely perfect. The most we needed was a light jacket in the mornings.

We visited Barcelona, Granada, Ronda, (Gilbraltar), Marbella, and then flew out of Malaga over to Morocco for a few days.

I'd go for the low airfare and the low crowds any day :)

But, weather can change from year to year. We left snow/ice (unusual for March) in Nashville and came home to total warm spring weather.

So, maybe we were just lucky with our Spain timing.

I am a schoolteacher and also travel about a week at a time. I did an Andalusia trip February 19-25, 2011, flying in and out of Madrid, and visiting Seville, Cordoba, and Granada. I went because the airfare was $572 round-trip (such a deal!) and had a great time. I was coming from chilly Michigan, so it was warm to me. (Anything above freezing would have been warm.) I wore a T-shirt and pants about half the time, and I put a fleece over that the other half. The only time I really remember being cold was when I went to the Alhambra and got there before sunup in order to get a ticket. I think you'd have a great trip either timeline. Enjoy!