Bus:
Snezhny Resort has its own direct bus that departs St. Petersburg on Saturday, Sunday and holidays at 9am from Moskovskaya metro (Aviatsionnaya st.), and at 10am from Ozerky metro (Vyborgskoe shosse, north). The journey takes about 2 hours from Ozerky and 3 hours from Moskovskaya and costs 80 R ($3) one way. The bus back to St. Petersburg departs Snezhny at 6pm.
There's also a regular bus # K-678 daily from Ozerki metro station in St. Petersburg (North). The bus departs Ozerki at 9am, 11am, 2.30pm, 4.30pm, 7.20pm, 9pm and takes about 1 hour 50 minutes to Korobitsyno (which is near Snezhny). The bus from Korobitsyno to St. Petersburg departs at 6.30am, 7.20am, 11.40am, 1.40pm, 5.10pm, 7pm, 9.40pm and also takes about 1 h 50 minutes.
Train:
Take a train to Sosnovo from Vyborsky station in St. Petersburg, and then from Sosnovo buses 645 or 646 or a taxi towards Korobitsyno. Stop at Snezhny resort. Total travel time about 2 hours. The local bus schedules are a mystery, so if unsure in your Russian skills, it's better to take a bus from Ozerki metro station.
Driving:
Take Vyborgskoe Shosse towards Finland. Turn right to Pervomaiskoye and drive up to Podgorie. Then turn right towards Michurinskoe. The resort is near Korobitsyno village. The driving time from St. Petersburg is 1 to 1.5 hours.
Flying:
The planes to St. Petersburg arrive to Pulkovo airport, which is quite far from the resort. You will need to go across the city and drive towards Vyborg. The whole journey takes about 4 hours.