The prize includes four round-trip plane tickets — coach — as well as a pair of two-night stays "at Albemarle Estate at Trump Winery," four tickets to "Trump Winery's Mother's Day Brunch," and ground transportation.
The National Republican Congressional Campaign, which is offering the prize, said the trip is worth about $2,850.
Politico first reported news of the contest, which began last Thursday and ends May 9.
At the very top of a web page promoting the contest, the NRCC, which supports Republican campaigns for the House of Representatives, said people can get a chance to win the prize by donating $10.
The site also then offers a chance "at this once-in-a-lifetime opportunity" for donors who contribute other amounts ranging from $25 up to $3,500.
But at the bottom of that web page, the NRCC notes, "NO PURCHASE NECESSARY TO ENTER OR WIN A PRIZE."
And the page also says: "Making a contribution does not increase your chances of winning."
However, when viewers are offered the opportunity to enter without donating, they are then transferred to another web page that says at the top: "Donate to Double Your Chances."
On that page, viewers can input their email address and cell phone number to be entered for the contest.
CNBC has reached out to the NRCC for comment on the contest, and on the claim that a donation will double an entrant's chances.
According to the contest rules, "ten (10) potential winners will be chosen by random drawing, from the pool of all eligible entries received during the Entry Period," on May 10.
"Sponsor may, at its discretion, conduct background checks on some or all of the potential winners to ensure they do not present security risks to the NRCC," the rules state. "The Sponsor will then select one (1) winner best representing, in the sole judgment of Sponsor, the NRCC's support across the country, and one (1) prize notice will be distributed."
To get their prize, the winner must give the NRCC permission to use photographs and recordings of the winners "in campaign promotional material or advertising."
The Trump Organization purchased the 1,300-acre estate containing the winery in 2011. The president's son, Eric Trump, is the winery's president.