YOU BET! But, first let me say not all headaches are created equal. A headache can simply be the result of stress that causes muscular tension the neck or as a result of inflamed sinuses from strong smells or a head cold. At the far extreme, a headache may be a sign of an life threatening intracranial hemorrhage. Ice or cold packs won't be of much help in these. I will restrict my answer to only migraines and even then migraines vary in terms of cause and treatment and as a medical worker I will advise you to have a neurologist eval just to be sure your chronic migraine isn't a brain tumor. Hopefully your doctor has cleared you of all but migraines, so, will ice or cold packs help and if so how well and by what mechanism.
A 2013 randomized, controlled, crossover clinical trial evaluated freezable ice packs applied to carotid arteries at the neck. Maximum pain reduction was observed at the 30 minute time point with a 31.8% ± 15.2% decrease in pain in the treatment arm compared to a 31.5% ± 20.0% increase in pain at the same time interval in the control arm. These findings confirm the application of a frozen neck wrap at onset of migraine headache targeting the carotid arteries at the neck significantly reduced recorded pain in participants with migraine headaches (P<.001)
Cryotherapy or cold may be so effective that the popular People's Pharmacy site even recommends eating ice cream or chugging cold drinks to alleviate migraines. https://www.peoplespharmacy.com/2015/04/06/see-how-brain-freeze-can-stop-a-migraine-headache-in-its-tracks/
And Scientific American states the mechanism may go beyond simple vasoconstriction of carotid and basilar arteries. https://blogs.scientificamerican.com/observations/brain-freeze-might-help-solve-migraine-mysteries/
There have been clinical studies testing cryotherapy devices for the treatment of migraines: https://clinicaltrials.gov/ct2/show/NCT01898455
But, this is something you can do without a corporate sponsor. My suggestion is to apply an ice pack at the nap of your neck (back of neck) not to your forehead. I find the if the therapy is going to work, you will achieve significant pain relief in just 5 minutes.