This is a great question. After all, if the purpose of fever is to fight infection, it stands to reason that suppressing fever weakens the body’s response to infection. And this reasoning has some experimental support – in both humans and animals, moderate fever seems to decrease the damage and mortality caused by infections [1] [2].
Given the prevalence of the common cold, and the prevalence of treating it with aspirin and ibuprofen, you’d think there would be lots of data that examine the effects of painkillers on colds. But there are not.
But to a first approximation, we don’t need well-designed clinical trials to tell us if there are strong effects of painkillers on cold symptoms or duration. Given the ubiquity of colds and painkiller treatment, big effects would have been obvious many decades ago. Formal studies are needed only to analyze more-subtle effects.
And subtle effects are all we see in the few trials that have been conducted. The most recent survey of the effect of non-steroidal anti-inflammatory drugs (NSAIDs, which include aspirin and ibuprofen) on colds includes only a few studies [3]. The results vary from study to study, but a few conclusions can be made.
It doesn’t seem likely that NSAIDs increase cold duration, which you would expect if they reduce clearing of viruses by the immune system
Cold symptoms were about a quarter-day shorter in duration with NSAIDs vs placebo. Given the noise in the data, this is not good evidence of decrease, but it is fairly strong evidence against an increase in the duration of symptoms.
There is better evidence of a positive effect on pain-related symptoms (headache, muscle ache) and less evidence of an effect on respiratory symptoms (cough, sneezing). In other words, pretty much what you would expect.
The bottom line is that there is no evidence that NSAIDs increase cold duration, and any effect is likely to be very small. Your best guide to treatment then is probably your own experience – if aspirin or ibuprofen make you feel better, go ahead and take them.
Footnotes
[3] Efficacy and safety of over-the-counter analgesics in the treatment of common cold and flu.