About 600 Rangers fans gathered outside the front of Ibrox before and after the abandoned game against Hearts in a noisy protest against the club’s board.
Fans’ groups had called for supporters to gather at the main entrance 45 minutes before Friday’s kick-off.
In the snow, they chanted slogans against shareholder Mike Ashley, who wants the stadium as security for a £10m loan, and the club’s directors.
Police Scotland say officers dealt with a disturbance outside the ground.
Video footage later emerged of scuffles and snowballs being thrown at the Argyle House entrance at the Govan stand.
There are no details yet about whether any arrests were made.
Police say the match was called off by referee Bobby Madden after 25 minutes “because of the deteriorating weather conditions”, and at that point several hundred fans convened again outside the main door.
They voiced their anger at Sandy Easdale, who is the chairman of the club’s football board, and his younger brother James, who is on the board of Rangers International Football Club.
The supporters, aware of the desperate cash shortage at the Scottish Championship club amid boardroom turmoil, were moved to organise a protest when news broke that Newcastle United and Sports Direct owner Ashley had offered a £10m loan, but wanted Ibrox Stadium and the Murray Park training ground as security for it.
Rangers had previously said they would never allow Ibrox to be used as security against a loan.
The club needs cash to meet the January wage bill. Ashley owns 8.92% of the shares but his attempt to increase that stake to almost 30% wasstymied by the Scottish Football Association.
The consortium comprising Douglas Park, George Letham and George Taylor, which owns 20% of Rangers, has said it will increase its offer of £5m in funding to avoid the board opting for Ashley’s cash.
“Rangers fans, including ourselves, do not want Ibrox given over as security to anyone,” said a spokesman for the consortium. which wants two board positions in exchange for the cash.
“There is absolutely no need when there are people ready and committed to offer more-than-adequate funding, while at the same time protecting the stadium.”
Prior to kick-off on Friday, news emerged that Dave King, who owns 15% of the shares, had lodged paperwork calling for a general meeting to remove all four directors from the Rangers board.
Many Rangers fans feel that the presence of Ashley’s associates Derek Llambias and Barry Leach on the Ibrox board mean the board, with the backing of chairman David Somers and James Easdale, will agree to Ashley’s loan offer.
Supporters’ group the Union of Fans claimed: “Derek Llambias and Barry Leach have been appointed by Mr Ashley to ensure he grabs the remaining assets of the club.”