SpinWall defaults to change your wallpaper every 30 minutes (approx). You can change this frequency, but it's not every minute. There is one download per cycle, so if you leave things stock, that's only two downloads per hour with each one taking a few seconds each. Additionally the downloads happen invisibly in the background where you'd likely not notice it at all.
Beyond the downloading, the SpinWall software is based on timer interrupt technology. It periodically checks if it's time to download a new wallpaper, but aside from that split second action every 10 minutes or so... SpinWall just idly sits by your clock and waits.
In short, SpinWall shouldn't slow down your computer at all. You'll barely notice it's presence.
