Mr Drakeford’s comments came as he announced that everyone in the top four risk categories in Wales will be offered their first vaccine dose by the weekend, making it the first nation in the UK to reach that milestone.
The first minister said reopening remained a “very big if” due to uncertainties surrounding new variants but the number of new infections reported in Wales is on a downward curve.
If that trend continues, Mr Drakeford added, then he can “see a path into spring” and may be able to “restore freedoms to people”.
Wales is currently under “Level 4” restrictions, which stipulate that people must only leave their homes for essential purposes such as work and exercise and pubs and restaurants remain shut.
Speaking to BBC Breakfast on Friday morning, Mr Drakeford said: “It’s a very big if because there are so many unknowns, new variants that are happening in different parts of the world that could make a difference here in the United Kingdom.
“But with vaccination, and with numbers falling, provided we reopen society carefully and cautiously and don’t allow the virus to get away from us again, we can see a path into the spring where it will be possible for us to go back to doing some of the things that we’re all missing so much.”
Mr Drakeford said Easter was an “important moment” for the tourism and hospitality industry in Wales and the government was “talking with them about what might be possible”.
The first minister said there were around 740,000 people who fell into the top four categories in Wales, some 689,000 of whom had been offered a first jab by Wednesday.
He said that number will have surpassed 700,000 by the end of Thursday. By Friday, Mr Drakeford added, there would only be a small number of people in the top risk groups that hadn’t been inoculated.
Friday’s announcement marks a turn around in fortunes for Wales. Less than a month ago it was the slowest out of the UK’s four nations in administering vaccines amid supply difficulties.
The Welsh government was forced to walk back comments on the programme by Mr Drakeford after he claimed a gradual rollout of its allocation of Pfizer jabs was necessary to ensure vaccinators were not “standing around with nothing to do for another month”.
On Friday morning, Mr Drakeford said Wales is expecting a “small dip in the volume of vaccine coming” in over the next two weeks.
But supply would pick up again by March and “that gives us confidence that we will complete the vaccination of the next five priority groups by this spring”.
“That’s what we promised we would do, we remain firmly on track to deliver that,” Mr Drakeford added.
Mr Drakeford said the Welsh Government was “confident” it would vaccinate the top nine priority groups by the spring and aimed to reach the rest of the population by the autumn.
“Plans are already being made because we will need the vaccination centres, we will need the staff to deliver it, we will need the systems to contact people and all of that is being worked on now,” he said.
Additional reporting by Associated Press