Yes, surely but depends on levels.
Senior level training budgets are reduced but not training per se i.e. the venue and facilities aren't 5-star hotels anymore (nor residential resorts) but in the office conference room itself (has it's disadvantages but ;-) trainings are happening and no cuts).
Similar is the situation for the mid-levels... the only hit is that people have been removed and therefore the no. of days engagement has been drastically reduced.
The entry-levels and the junior level freelance trainers have been hit the most. No more bulk trainings... in many companies either being done by internal trainers or by functional heads.... outsourced trainers have been hit.
Some companies have smartly started hiring full-time trainers so that a fixed salary could be paid and not per-day rates.
This is the India perspective.