Can ice help bring down blepharitis swelling & does the swelling ever go away?

It is most important to get evaluated by an oculoplastic surgeon or opthalmologist who treats your condition frequently as you typically require antibiotic therapy at minimum. 

Thank you for the question.Cold compresses are not known to be useful to treat blepharitis. Eyelid scrubs, warm compresses, topical and oral antibiotics are the standard of care. Make a consultation with a specialist for evaluation and treatment. Good luck.

Don't want to use ice.  Warm is always best to help soften the secretions and hopefully make them easier to express.  If not improving you may benefit from low dose Doxycycline which helps with the inflammation and the secretions.  

You can try ice.  It will likely not do much.  I would consult with an Ophthalmologist to see if he or she recommends any additional treatments.  Good luck.