I have a 99 olds Bravada that I love

I have a 99 olds bravada that I love. However, whenever the outside temp gets down below say even 40 it will not start. It cranks, but sounds like there is no fuel getting where it needs to go. For awhile, if we just turned the key to 'on' for a bit before trying to start it that would help. It would chug at first and die then we would have to leave the key 'on' for a bit again until it would finally start. After that first problem in the morning, it would pretty much do well through the day. When the weather was nice, we didnt have any problems with it starting. As soon as it started getting colder the problem reappeared. We had the fuel pump replaced in march, but were still occassionally running into this same issue, but it was only on the first start of the day and when the weather outside was cooler. Now that it is winter-time, it will not start again. Could it be a water temp sensor or a bad pump or what the heck. I would really love to drive this thing, I did not buy it for use as a lawn ornament :) thank you for any ideas you may have. Tanya