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Influential youngster Josh Magennis, making his first ever league start for Cardiff, saw his header smack the underside of the crossbar midway through a first half which the hosts dominated.
But Blackpool almost exclusively bossed matters after Charlie Adam had fired them level just 28 seconds after the restart.
Both sides had chances to claim victory but the draw leaves the hosts in fourth spot, while Pool remain three points behind but move to within a place of the play-offs.
Cardiff staff worked wonders clearing snow and ice from the ground and surrounding areas in order to get the game on as the big freeze played havoc with Britain's sporting calendar.
And their endeavours were rewarded as Hudson headed an early opener.
Peter Whittingham whipped in a deep inswinging free-kick from the right that keeper Paul Rachubka came for but failed to collect, and Hudson was on hand to head home at the far post.
The hosts imposed themselves on proceedings in the first half and 19-year-old Magennis came within inches of a goal on his full debut when he headed against the bar in the 25th minute, before strike partner Ross McCormack looped a good chance onto the roof of the net shortly after.
But Magennis' afternoon was to end on a sour note 10 minutes before the break when he was forced off with an ankle injury.
Whittingham whistled a 25-yard free-kick narrowly over while Cardiff keeper David Marshall, who had little to do the first half, did well to hold Ben Burgess' header and ensure the home side held their narrow advantage at the break.
The hosts were made to pay for not making the most of their dominance as Blackpool wasted no time levelling matters after the restart.
Brett Ormerod found Adam in the penalty area and he slotted into the bottom corner from close range.
The Seasiders gained confidence from their breakthrough and were soon completely in the ascendancy as Cardiff struggled to get a grip on the second half.
Burgess and Neal Eardley both forced saves from Marshall before the former found the roof of the net with another header as Blackpool threatened to score a second.
Imposing frontman Burgess had already enjoyed several chances when he blasted the best of the lot over the bar from just six yards.
The away side's dominance forced Cardiff boss Dave Jones to switch to a 4-3-3 formation to match their opponents.
The change had the desired effect as his charges regained some kind of foothold in the game with chances coming at either end.
But neither side could find a winner, with Marshall denying Burgess for an umpteenth time when he managed to keep out his 87th-minute effort while Rachubka tipped Whittingham's late effort over the bar.
Source: Team Talk
Source: Team Talk