Do warming filters still make sense on a digital camera like the Canon 450D?

Some, yes. Most of the time filters are not needed, but sometimes they can make a visible difference. The reason why color correction filter can make the difference is that on digital cameras color correction is done after the image has been captured to the sensor, and often after it has already been digitized.

If the color correction is done before A/D conversion, not using color-correction filter means you get more noise to the channels that were compensated in color correction. So, for example, if you took your shot in very orange street light, your blue channel will go only to some 25-50% of the maximum value. This in turn means that when the blue channel is amplified to correct white balance, the sensor noise on that channel gets amplified 2-4 times more than it would have been if you had used proper filter.

Not all noise is amplified even if the white balance is corrected after recording the image to sensor, but it goes beyond scope of this question. See this question to learn more: What is noise in a digital photograph?

If the color correction is done after A/D conversion all the above is true, but in addition you can get some banding to the image. For example, your blue channel values might now be mapped from 0 to 63 instead of 0-255, and this when it's multiplied to balance colors, you get on average three "unused" values between each actual value. This shows as banding, ie. gradients are not smooth, but color changes in steps.

Using the filter obviously reduces the amount of light hitting your sensor, so you need longer exposure time to compensate. So it can be a tricky trade-off sometimes. Also, if you are shooting with ISO level where your camera has lot of S/N headroom, it might not be worth the effort.

However, if the point is to skew the colors, ie. get artistic results by coloring the scene differently, this can as well be done on computer at post processing stage. During capture it's often best to aim to capture the scene as well as you can, ie. capture all the information you can get as accurately as you can. This then enables you to choose, and change your mind, later about how to distort and skew the image for artistic effects. You can of course get make the effect all with filters, then you just lose the ability to change your mind later.

If your aim is to get technically as good results as you can, color correction filters can make sense. If your aim is to keep the art of analog photography alive, then color-changing filters can make sense. And these apply to lenses; for flashes the rules are all different.

So if your aim is to learn and revive the secrets of old school photography, go for it; just do it knowing you can lose information that way. So, on shots that you can't easily retake trying to get the information as cleanly as possibly to the memory card and applying artistic touches later on often makes more sense.