Can you train with a cold? The 'above the neck' rule
A simple rule of thumb many sports doctors use to decide 'train or not' with a minor illness is called the above-the-neck rule. If symptoms are limited to above the neck — stuffy nose, mild throat tickle, sneezing — without fever and without a general run-down, achy feeling in the body, light-to-moderate training is usually safe, and some evidence suggests it can even ease symptoms slightly by temporarily improving nasal breathing and mood.
If symptoms extend below the neck — muscle and joint aches, a chest cough, diarrhea, nausea — or come with a fever, training should be postponed entirely. Physical exertion during a systemic infection with fever adds extra stress to an immune system and cardiovascular system already working overtime fighting the infection — in rare cases, intense training during a viral infection that involves the heart is linked to a risk of heart muscle inflammation.
The rule doesn't replace common sense or a doctor's advice for serious symptoms, but it gives a reasonable guideline for the common 'I've got a bit of a cold, not sure if I should train' situation — focus on where the symptoms are, not just the fact that you feel unwell.