BOSTON — Gov. Charlie Baker formally asked the federal government Friday to declare a disaster in 10 Massachusetts counties after a relentless series of winter storms brought record snowfall and frigid temperatures, causing 25 deaths and costing the state and its cities and towns an estimated $400 million. The request was made in a 22-page letter to President Obama, delivered through the acting regional administrator of the Federal Emergency Management Agency. Citing an “unprecedented and disastrous pattern of severe winter weather,” the letter seeks 75 percent federal reimbursement for snow removal and other costs related to the storms, which Baker is asking FEMA and the president to treat as a single, monthlong disaster. “Despite our experience in dealing with harsh winter conditions, this severe pattern brought (Massachusetts) to a virtual standstill for days at a time,” Baker wrote.