Striker Tudgay cut his toe on a glass at a family party over the weekend and sustained tendon damage - an injury which could keep him out for months if it is quite severe.
Defender Wood has re-damaged his troublesome groin which put him out for the back end of last season after making a tackle in training.
New winger Small meanwhile has a slight tear in his calf at it is expected he will be out for at least a fortnight.
Paul Sturrock is hoping that the players are ready to return for the start of the season although he thinks that Wood's layoff could be the longest.
Meanwhile JP McGovern has joined Drissa Diallo at MK Dons after signing a three-year deal and Craig Rocastle has completed his move to Oldham Athletic penning a two-year contract.