Nope. Barry was in the WWF as The Widowmaker beginning 1989 and was off television by the end of that year. He worked a house show in January 1990 and then was back to WCW. I know this for a fact because Windham was a part of the reformed Horsemen in 1990/1991 that featured one of my favorite spots in wrestling when JYD returned to WCW and challenged Ric Flair thanks to Rocky King. Match was terrible, but it was really fun.
Windham was part of the Horsemen with Flair/Arn/Barry/Sid Vicious with Ole Anderson working as their manager for parts. (This was during the time Sting was a member and got turned on by the Horsemen)
Windham never worked the WWF at the same time Flair did and Flair never impacted his decision to stay or leave the WWF. He did benefit from Flair leaving WCW though as he got catapulted into the title scene, but many fans, despite loving Windham, absolutely rejected it as they felt it was cheap for him to just jump into Flair's spot.
Windham would have bad luck because when Flair would come BACK to WCW, Windham was seriously hurt (shredded knee) around the same time and would try to come back at Slamboree 94 to face Flair and hurt himself again. That's why he disappeared for awhile and came back in the WWF as a much slower version of himself.
So to be clear, Flair's run in the WWF from 1991 to 1993 had no other members of the Horsemen on the WWF payroll for any period, nor any period 6 months earlier or after.
Would have been interesting though. Would Vince have ignored that history all together?
The Horsemen started as full blown group with their broken leg steel cage beatdown on Dusty Rhodes in Aug 1985 (Flair was a face at the time, he had been linked in minor ways to The Andersons in past storylines, but even as a face he never was friendly wit Dusty) - They were comprised of Flair, Ole & Arn Anderson, Tully Blanchard and TB's manager JJ Dillon
That group stayed in tact from Aug 85-Jan/Feb 87 when a dispute between Ole & Blanchard lead to Ole's dismissal and subsequent face turn. He was replaced by Lex Luger.
Flair, Luger, Blanchard and Arn worked as a group with Dillon from Feb/March 87- Jan 88 when Luger left the group in a dispute over his place following a Bunkhouse Stampede Match. Barry Whyndam, a fierce opponent of The Horsemen and especially Flair, was recruited to take his place. he declined initially, even teaming with Luger to win the World Tag Titles from Tully & Arn at The Clash Of Champions in March 1988, but eventually accepted. He helped Tully & Arn regain the tag titles and Dillon helped him beat Dusty Rhodes for the US Title a short time later. He joined the group around April 1988
Flair, Whyndam, Tully & Arn ran from April 88-Oct 88 when a contract dispute and several issues regarding Dusty Rhodes behind scenes work as Head Booker lead to Tully & Arn leaving for WWE. Flair & Whyndam remained a duo, eventually taking on a new manager in early 1989 (Hiro Matsuda). Whyndam left WCW for WWE shortly after the Super Brawl PPV in Feb 89 (where Steamboat beats Flair for the World Title). Flair turned face a short time later and teamed with Sting for much of 1989 and there was no Four Horsemen.
WCW offered to resign Tully & Arn in late 1989 but Blanchard's failed drug test caused WCW to rescind their offer (he was fired from WWE as well). Arn decided to return to WCW since Blanchard was gone and his value diminished in WWE but WCW lowered his financial offer considerably without Blanchard. He returned (with a now retired Ole, last seen in the spring of 87 feuding with The Horsemen) around Oct/Nov 1989 and re-united the group, soon asking Sting to join as the 4th member.
Flair, Ole & Arn, & Sting ran as a group from roughly Dec 1989-Jan 1990 when The H-Men turned on Sting after he was awarded (and accepted) a title match vs Flair at the upcoming PPV. Barry Whyndam returned from WWE and Sid arrives from USWA/Mid South shortly after and they fill out the group with Ole strictly as a manager/adviser. This group lasts from roughly Feb/March 90-Dec 90/early 91. Sid disappears around this time (headed for WWE). Ole basically disappears from TV by the fall of 1990.
The Horsemen are still a group of sorts but Flair is mostly on his own in early and mid 1991 until he leaves for WWE. Whyndam and Arn are involved in their own storylines with little interaction with Flair and while they remain friendly on screen they are not strictly presented as a group consistently. They do have some moments, particularly the brutal 1991 War Games match (Sid was still there for that) in Feb 91.
Most of the attempts to re-unite the group fall flat in 1993 (remember Paul Roma ??) and in fact The H-Men are not a group when Hulk Hogan arrives in WCW in the summer of 1994. Flair turns heel to oppose Hogan, but The Horsemen as a unit do not officially re-unite until late 1995 when Flair & Arn start recruiting "young blood" bringing in Brian Pillman & Chris Benoit. Pillman is out of the group by the spring of 96 but former NFL star and WCW broadcaster Steve McMichael replaces him with Flair, Arn, and Benoit as the core of the group from spring 96 through Oct 97.
Flair disbands the group in the fall of 97 to pursue his personal fued against Curt Henning and Hulk Hogan, now in the NWO and working as the company's top heels (Flair is a face at this point, Benoit a face by association, and Arn retired due to injury). The group re-unites, adding Dean Malenko as an active member (with Arn in a managerial capacity) in Sept 98 and remains until April/May 99 when Benoit & Malenko leave after a dispute with Flair over how they are being booked (he was the onscreen WCW President at this time and they were portrayed in stories as being treated poorly by him in his new power role).
After that there really was no Horsemen. Flair & Luger united to form Team Package in 2000 but there was never a full fledged Horsemen reunion. Arn occasionally appeared onscreen with Flair in WWE but was clearly retired and his appearances were brief and infrequent. They essentially survived as a group with Flair and Arn as anchor members from Aug 85-May 99 with a bout 2 years of inactivity in between.