Sometimes it depends on what we mean by being Vitamin D deficient. Vitamin D is a fat soluble vitamin and can be stored in fat tissues. What they have measured in determining your D status is your circulating levels which may be low.
The prescription from your Doctor should not be D2 but D3 anyway.
I wouldn't worry too much and go ahead with your fast. Sunbathing is fine in moderation while fasting, but you will have to rely on supplementation once the fast is over, if sunlight is absent, as it will be here in the UK for the next 5 months or so.
As Hopinso has posted, she feels the cold terribly while fasting in the Winter, with sub-zero outside temperatures; chilling and feeling cold inhibits and prevents elimination and can be very enervating.