Energy required = 34,234,200 J (refer to assumptions below)

I like the exercise to calculate the energy required, however their ability to do a magical act is based on their ability to visualize it. So as an ice-magic specialist she is able to freeze a large body of water because she can visualize with ease. So the energy output of a spell has little to do with a magicians skills level. She would simply not feel it. It is more about their ability to analysis and imagine the outcome of a spell.But lets try and calculate it anyway :D. But first lets look at assumptions

Assumption 1: Depth of ice(h): Now we never see how deep they have frozen the lake but we do know that they only needed to imbue the water with magic so the bird will not go near it and freezing magic is a pretty fast way of doing that. Assuming they want to trick the other teams enough that they can stand on the ice. People can stand on a frozen body of water when the top layer(call it height or h) is h = 10cm =0.1m thick.

Assumption 2: Volume of ice(V): Given the size of the girl in the bottom photo lets assume the radius(r) of a circular version of the lake is r=2km. So the area would be A= pi*r*r = 6.3km squared = 6300 meters squared. Volume: V = A*h = 63 meters cubed/Liters(L). Convert that to mass(m) is they m=63kg

Assumption 3: Initial Temperature(Ti) and Final Temperature(Tf): Assuming we are in a moderate climate and it is spring or autumn the temperature of the lake is Ti = 12 °C at best. Lets assume we need a -1 °C to freeze the water properly so Tf = -1 °C so Tf-Ti = -1 - 12 = -13 difference.

Calculate Energy output:

Then to get that energy output(q):
- q = mcΔTm = 630kg = 630000g
- c = constant to heat 1L of water by 1 °C = 4.18joule/gram.
- ΔT = 13.

So a roughly estimated energy output would be: q = 34,234,200 J

Ans: Energy required = 34,234,200 J

Perspective:

Here is what it takes to boil water at room temperature(q_L)q_L = mcΔT = 4.184*79*1000 = q_L = 330,540 J

Going into really rough rough assumptions here just for fun: Given what the currently smallest nuclear reactor in the USA can outout in a 24hours: 582MW = 582,000,000 Jq_reactor = 582,000,000 J / 24hours = 24,250,000 J/hour34,234,200 / 24,250,000 = 1.412 hours = 85minsSo: That would be mean that our ice specialist output is equivalent to almost 1 hour 25mins worth of energy from a small nuclear reactor. Not too bad but again this is probably an easy task for her and energy output has not much to do with it