wood framed windows - water leaking inside house

We have a 100 yr old stucco house we purchased two years ago. It has mostly wood framed windows. This year when the weather started to warm up we found water was entering the house onto our newly installed hardwood floors :( It has been suggested this may only happen when there is 'ice damming' ??
It did not happen last year. Our eaves are overdue to be redone so would this be a factor? I have noticed the only windows it happens on are the ones without flashing. Is there a way to remove the brickmold and install flashing without removing and reinstalling the windows?
Thanks, Shaynelle
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