Neither the lawmakers nor the lobbyists attending the events want to talk about them, even though such trips are permitted under the law. They allow members of Congress to hit hot spots like the Napa Valley wine country, famed golf courses and hunting preserves, as well as five-star hotels in Puerto Rico, Las Vegas, South Florida and even Bermuda.

Congress, after a corruption scandal that involved golf trips to Scotland and other getaways paid for by lobbyists, passed legislation in 2007 prohibiting lobbyists from giving lawmakers gifts of just about any value. But as is the norm in Washington, the lawmakers and lobbyists have figured out a workaround: Political campaigns and so-called leadership PACs controlled by the lawmakers now pay the expenses for the catering and the lawmakers’ lodging at these events — so they are not gifts — with money collected from the corporate executives and lobbyists, who are still indirectly footing the bill.

Even if no explicit appeals for help are made, the opportunity to build a relationship with the lawmakers, staff members and family — far from the distractions of Washington — is worth the price of admission, the lobbyists said. The donors and lobbyists, 50 to 100 of whom typically attend the events, generally donate individually or through a corporate political action committee between $1,000 and $5,000 apiece, in addition to paying their own hotel bills and airfare. There is no public disclosure that specifically shows how much is raised at each event, and lawmakers are generally unwilling to say.

“An informal setting is an effective way to build a better relationship,” said a health care lobbyist who attended the fund-raising weekend in Vail this month. The event included five House Republicans, none of them from Colorado and two of whom serve on the powerful Energy and Commerce Committee, which oversees the health care industry. “It’s a way to get some large chunks of a lawmaker’s time,” the lobbyist said.

One Republican campaign consultant, Mike Gula, sent lobbyists a save-the-date summary in December that featured 30 trips in 2014, such as a “Spa Weekend Trip” in Las Vegas in March sponsored by Representative Ann Wagner, Republican of Missouri.